The 32-year-old Englishman made the last of his 17 appearances this season in December, the day he told the BBC he would apply to be their manager.
Alloa seven days later appointed Jack Ross to succeed Danny Lennon.
And the Scottish Championship club say Chopra has now been released following "set-backs" after picking up an injury.
Chairman Mike Mulraney thanked Chopra for "his great effort" in helping the Wasps avoid relegation last season, when they defeated Forfar Athletic in a play-off after finishing second bottom.
But Alloa are presently 10 points adrift of Livingston at the foot of the Championship and automatic relegation looks a certainty this time with only seven games of the season remaining.
Chopra joined Alloa almost exactly a year ago after leaving Indian club Kerala Blasters and went on to make 28 appearances, scoring four goals.
However, only one of them came this season - in August against Rangers - and his last outing came as he was substituted through injury after 29 minutes of a 5-0 thrashing by Championship rivals Dumbarton in the Scottish Cup on 8 December.
Chopra began his career with Newcastle and went on to play for Watford, Nottingham Forest, Barnsley, Cardiff City, Sunderland, Ipswich Town and Blackpool.