Jakupovic will return to the KC Stadium to provide competition for Steve Harper while McGregor serves his three-match ban.
The Bosnian-born Switzerland international made four appearances for Orient and kept three clean sheets, as the Sky Bet League One promotion challengers won all four contests.
"We'd like to thank Eldin for all his efforts here over the last few games and he's done a fantastic job," O's boss Russell Slade told the club's website.
"It's unfortunate for us but the process of finding a replacement has already started."
- Sports & Recreation
- Allan McGregor
- Steve Harper