Here's a function I wrote that does exactly this. Pass the handle of the msgbox() and the fontsize to the function.
If you don't want a function, here's the basics:
First get the handle to the text within the message box, then change the font size. Here's a demo.
mh = msgbox('I can barely read this.', 'test');
th = findall(mh, 'Type', 'Text');
th.FontSize = 14;
If you increase the font size too much, you'll need to expand the message box to fit the extent of the text.
deltaWidth = sum(th.Extent([1,3]))-mh.Position(3) + th.Extent(1);
deltaHeight = sum(th.Extent([2,4]))-mh.Position(4) + 10;
mh.Position([3,4]) = mh.Position([3,4]) + [deltaWidth, deltaHeight];
Lastly, allow the user to resize the window if needed: