The 25-year-old centre-back has made almost 100 appearances for the Gresty Road outfit and will add some much-needed defensive cover to Ronnie Moore's side.
The Whites boss was only able to name four substitutes for the midweek Capital One Cup clash with Bolton and Moore is thankful to Alex for sanctioning the deal.
"I'm really pleased to be able to bring Adam in," the former Rotherham boss told the club's official website.
"He can play on either side of the centre of defence, he's big and strong and good in the air.
"I'd like to thank Crewe manager Steve Davis for allowing Adam to join us."