The 26-year-old suffered the injury in the 52nd minute of Gloucester's Aviva Premiership defeat at Worcester, with subsequent scans revealing he now faces up to six months on the sidelines.
Morgan, who signed his first professional deal at the club in 2004, has been a key man in the Gloucester line-up this season.
He has scored five tries in 16 appearances, helping the Cherry and Whites stay in touch for the race for a top-four finish.
However Morgan's injury means Gloucester are now short of options for the full-back jersey - with coach Bryan Redpath likely to bring in cover for the rest of the season.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.