Macro expansion inside \href

Expand the string substitution first by storing it in an argument, which you can then use with hyperref's \href:

\documentclass{article}

\usepackage{xstring}
\usepackage{hyperref}

\newcommand\phone[1]{%
  \StrSubstitute{#1}{ }{}[\firstarg]% Store first substitution in \firstarg
  \StrSubstitute{#1}{ }{\,}[\secondarg]% Store second substitution in \secondarg
  \href{tel:\firstarg}{\secondarg}% Use stored arguments in \href
}

\begin{document}

\href{tel:0123456789}{01\,23\,45\,67\,89}

\phone{01 23 45 67 89}

\end{document}

The xstring commands are not expandable so can't in general be used inline in other commands. You can use a simple expandable replacement here.

\documentclass{minimal}


\usepackage{hyperref}

\makeatletter
\def\zza#1 {#1\zza}
\def\zzb#1 {#1\,\zzb}
\newcommand\phone[1]{{\def\!##1{}\def\$##1##2{}\href{tel:\zza#1\! }{\zzb#1\$ }}}
\makeatother

\begin{document}

    \href{tel:0123456789}{01\,23\,45\,67\,89}

    \phone{01 23 45 67 89}

\end{document}

You can't use \StrSubstitute in those places, because it doesn't produce the string after the substitution, but rather a fairly complicated set of instructions to produce that string.

A more complicated solution that avoids the need to input spaces between pairs of digits, so it will work even if you forget them.

\documentclass{article}

\usepackage{xparse}
\usepackage{hyperref}

\ExplSyntaxOn

\NewDocumentCommand{\phone}{m}
 {
  \dlichti_phone:n { #1 }
 }

\tl_new:N \l_dlichti_phone_href_tl
\tl_new:N \l_dlichti_phone_print_tl

\cs_new_protected:Nn \dlichti_phone:n
 {
  \tl_set:Nx \l_dlichti_phone_href_tl { #1 }
  % remove all spaces
  \tl_replace_all:Nnn \l_dlichti_phone_href_tl { ~ } { }
  % save a copy
  \tl_set_eq:NN \l_dlichti_phone_print_tl \l_dlichti_phone_href_tl
  % insert a thin space between any pair of digits
  \regex_replace_all:nnN
   { ([0-9][0-9]) } % two digits followed by another digit
   { \1\c{,} } % the same with \, in between
   \l_dlichti_phone_print_tl
  % remove the trailing \,
  \regex_replace_once:nnN { \c{,} \Z } { } \l_dlichti_phone_print_tl
  \dlichti_phone_href:VVV
   \c_colon_str
   \l_dlichti_phone_href_tl
   \l_dlichti_phone_print_tl
 }
\cs_new_protected:Nn \dlichti_phone_href:nnn
 {
  \href{tel#1#2}{#3}
 }
\cs_generate_variant:Nn \dlichti_phone_href:nnn { VVV }

\ExplSyntaxOff

\begin{document}

\phone{01 23 45 67 89}

\phone{0123456789}

\end{document}