I didn’t really like the currently most popular answer because it significantly changes the formatting of the message in the dialog.
Here’s a solution that will linkify your dialog text without otherwise changing the text styling:
// Linkify the message
final SpannableString s = new SpannableString(msg); // msg should have url to enable clicking
Linkify.addLinks(s, Linkify.ALL);
final AlertDialog d = new AlertDialog.Builder(activity)
.setPositiveButton(android.R.string.ok, null)
.setIcon(R.drawable.icon)
.setMessage( s )
.create();
d.show();
// Make the textview clickable. Must be called after show()
((TextView)d.findViewById(android.R.id.message)).setMovementMethod(LinkMovementMethod.getInstance());