He has since battled back to fitness and spent a month on loan at his former club Barnet earlier this season.
Sinclair, who will be out of contract at The Valley in the summer, should be in the Grimsby squad for Saturday's League Two trip to Aldershot.
The Addicks have extended striker David Mooney's loan spell until the end of the season.
Meanwhile, Paris Cowan-Hall has re-joined Grimsby on loan from Portsmouth for the rest of the season.
The 19-year-old striker was recently signed on a one-month loan but returned to the Premier League club after contracting glandular fever.