The 32-year-old, who joined Exeter from their Premiership rivals Bath last summer, made just seven appearances for the Chiefs.
Short's season was halted when he broke his leg playing against London Irish last September.
He underwent successful surgery before embarking on a lengthy rehabilitation programme that culminated in him briefly returning to action in late January.
But Short said: "I have been trying to get back, but it has been a struggle.
"Obviously it's disappointing to go out this way, but it is part and parcel of the game.
"As a player you tend not to really think about the end, but since the injury in September it has given me time to think about the future and get a few bits and pieces in place.
"As hard as I've worked, there was still too much pain and it has been a real struggle to get back to the same levels as I was earlier in 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.
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.