How to set the min and max height or width of a Frame?

There is no single magic function to force a frame to a minimum or fixed size. However, you can certainly force the size of a frame by giving the frame a width and height. You then have to do potentially two more things: when you put this window in a container you need to make sure the geometry manager doesn't shrink or expand the window. Two, if the frame is a container for other widget, turn grid or pack propagation off so that the frame doesn't shrink or expand to fit its own contents.

Note, however, that this won't prevent you from resizing a window to be smaller than an internal frame. In that case the frame will just be clipped.

import Tkinter as tk

root = tk.Tk()
frame1 = tk.Frame(root, width=100, height=100, background="bisque")
frame2 = tk.Frame(root, width=50, height = 50, background="#b22222")

frame1.pack(fill=None, expand=False)
frame2.place(relx=.5, rely=.5, anchor="c")

root.mainloop()

A workaround - at least for the minimum size: You can use grid to manage the frames contained in root and make them follow the grid size by setting sticky='nsew'. Then you can use root.grid_rowconfigure and root.grid_columnconfigure to set values for minsize like so:

from tkinter import Frame, Tk

class MyApp():
    def __init__(self):
        self.root = Tk()

        self.my_frame_red = Frame(self.root, bg='red')
        self.my_frame_red.grid(row=0, column=0, sticky='nsew')

        self.my_frame_blue = Frame(self.root, bg='blue')
        self.my_frame_blue.grid(row=0, column=1, sticky='nsew')

        self.root.grid_rowconfigure(0, minsize=200, weight=1)
        self.root.grid_columnconfigure(0, minsize=200, weight=1)
        self.root.grid_columnconfigure(1, weight=1)

        self.root.mainloop()

if __name__ == '__main__':
    app = MyApp()

But as Brian wrote (in 2010 :D) you can still resize the window to be smaller than the frame if you don't limit its minsize.