The accepted answer worked well in 2015, but now better solutions exist.
For this problem issue #3368 was created and based on the solution provided by a Facebook employee working on React, react-string-replace was created.
Using react-string-replace, here is how you can solve your problem
const reactStringReplace = require('react-string-replace');
const HighlightNumbers = React.createClass({
render() {
const content="Hey my number is 555:555:5555.";
return (
<span>
{reactStringReplace(content, ':', (match, i) => (
<div className="spacer"></div>
))}
</span>
);
},
});