How to add onclick event to a string rendered by dangerouslysetInnerHtml in reactjs?

Caveat: This sounds like an X/Y problem, where the underlying problem (whatever it is) should be solved differently, so that you don't have to add a click handler to a DOM element created via dangerouslySetInnerHTML (ideally, so you don't have to create DOM elements via dangerouslySetInnerHTML at all). But answering the question you asked: (You've clarified the use case; solution #1 below applies and isn't poor practice.)

I don't think you can do that directly. Two solutions I can think of:

  1. Use delegated event handler on the div: Add a click handler on the div, but then only take action if the click passed through the b element.

  2. Use a ref on the div, and then hook the click handler up in componentDidMount and componentDidUpdate (finding the b element within the div via querySelector or similar), something along these lines:

Here's an example of #1:

<div onClick={this.clickHandler} dangerouslySetInnerHTML={this.createMarkup(string)}/>

...where clickHandler is

clickHandler(e) {
    // `target` is the element the click was on (the div we hooked or an element
    // with in it), `currentTarget` is the div we hooked the event on
    const el = e.target.closest("B");
    if (el && e.currentTarget.contains(el)) {
        // ...do your state change...
    }
}

...or if you need to support older browsers without ParentNode#closest:

clickHandler(e) {
    // `target` is the element the click was on (the div we hooked or an element
    // with in it), `currentTarget` is the div we hooked the event on
    let el = e.target;
    while (el && el !== e.currentTarget && el.tagName !== "B") {
        el = el.parentNode;
    }
    if (el && el.tagName === "B") {
        // ...do your state change...
    }
}

...and where you bind clickHandler in the constructor (rather than using a property with an arrow function; why: 1, 2):

this.clickHandler = this.clickHandler.bind(this);

Live Example:

let string = "Hello <b>Click here</b>";
class Example extends React.Component {

    constructor(props) {
        super(props);
        this.state = {
            clicks: 0
        };
        this.clickHandler = this.clickHandler.bind(this);
    }

    clickHandler(e) {
        // `target` is the element the click was on (the div we hooked or an element
        // with in it), `currentTarget` is the div we hooked the event on
        // Version supporting older browsers:
        let el = e.target;
        while (el && el !== e.currentTarget && el.tagName !== "B") {
            el = el.parentNode;
        }
        if (el && el.tagName === "B") {
            this.setState(({clicks}) => ({clicks: clicks + 1}));
        }
        // Alternative for modern browsers:
        /*
        const el = e.target.closest("B");
        if (el && e.currentTarget.contains(el)) {
            this.setState(({clicks}) => ({clicks: clicks + 1}));
        }
        */
    }

    createMarkup = value => { 
        return { __html: value };
    };

    render() {
        const {clicks} = this.state;
        return [
            <div>Clicks: {clicks}</div>,
            <div onClick={this.clickHandler} dangerouslySetInnerHTML={this.createMarkup(string)}/>
        ];
    }
}

ReactDOM.render(
    <Example />,
    document.getElementById("root")
);
<div id="root"></div>

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/16.6.3/umd/react.production.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/16.6.3/umd/react-dom.production.min.js"></script>

Here's an example of #2, but don't do this if A) You can solve the underlying problem separately, or B) #1 works:

let string = "Hello <b>Click here</b>";
class Example extends React.Component {

    constructor(props) {
        super(props);
        this.state = {
            clicks: 0
        };
        this.divRef = React.createRef();
        this.hooked = null;
        this.clickHandler = this.clickHandler.bind(this);
    }

    clickHandler() {
        this.setState(({clicks}) => ({clicks: clicks + 1}));
    }

    hookDivContents() {
        // Get the b element
        const b = this.divRef.current && this.divRef.current.querySelector("b");

        // No-op if it's not there or it's the same element we have hooked
        if (!b || b === this.hooked) {
            return;
        }

        // Unhook the old, hook the new
        if (this.hooked) {
            this.hooked.removeEventListener("click", this.clickHandler);
        }
        this.hooked = this.divRef.current;
        this.hooked.addEventListener("click", this.clickHandler);
    }

    componentDidMount() {
        this.hookDivContents();
    }

    componentDidUpdate() {
        this.hookDivContents();
    }

    createMarkup = value => { 
        return { __html: value };
    };

    render() {
        const {clicks} = this.state;
        return [
            <div>Clicks: {clicks}</div>,
            <div ref={this.divRef} dangerouslySetInnerHTML={this.createMarkup(string)}/>
        ];
    }
}

ReactDOM.render(
    <Example />,
    document.getElementById("root")
);
<div id="root"></div>

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/16.6.3/umd/react.production.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/16.6.3/umd/react-dom.production.min.js"></script>

Refs are an "escape hatch" giving you direct DOM access. Don't use refs lightly; usually, there's a better choice.

But again: I would solve the underlying problem, whatever it is, differently.