The 33-year-old is thought to have become the highest-paid player in world football when he made the move, signing a deal worth £630,000 a week in wages alone, but has since made just 13 appearances and scored three goals for the side.
Shanghai have endured a terrible season on the pitch, losing 12 of their 24 games so far, and new manager Wu Jingui dropped Tevez upon his appointment last week, accusing the former Manchester City striker of being too "overweight" to play.
"Our intention was to bring in an influential star player with high quality, and we all think Tevez could fit the bill," chairman Wu told a Shanghai TV channel.
"However, due to a lack of winter training and match fitness, he didn't meet our expectations."
During his previous spells with City, Manchester United and Juventus, Tevez boasts three Premier League titles, two Serie A titles and a Champions League among his individual honours.