The centre-back, who made his Wales debut in last week's 3-1 win against Cyprus, quit the Racecourse Ground for the Dons in the summer of 2005.
With Wrexham currently without defenders Steve Evans (dead leg), Shaun Pejic (Achilles) and Lee Roche (hamstring), Morgan makes a welcome return.
Dons boss Martin Allen said he was keen for the 21-year-old to gain regular first-team football during his return to the Racecourse Ground.
Morgan did not play in Saturday's game between Wrexham and Dons but should feature for the Dragons in Tuesday's Johnstone's Paint Trophy tie with Rochdale.
He said: "I'm delighted at the opportunity and after travelling up to Wrexham on Saturday with the first team it was good to meet some old friends again. I got a good reception from people inside the club and I'm now looking forward to the next month and playing again."