Carroll trained with the club's first-team squad on Tuesday for the first time since undergoing knee surgery in February.
The 28-year-old France international collided with Tomkins in the 76th minute at the Emirates and appeared to be dazed by the clash.
West Ham United capitalised on mistakes by new Arsenal new goalkeeper Petr Cech to secure a surprise 2-0 Premier League victory at the Emirates.
Newcastle secured their Premier League status with a 2-0 victory on Sunday over West Ham.
Newcastle United's disastrous season will come to a close on Sunday with the north-east club needing a victory against West Ham United to guarantee Premier League survival.
Manchester City playmaker David Silva was taken to hospital after sustaining an injury to his cheek bone during the 2-0 Premier League victory over West Ham United on Sunday.
West Ham United won 5-3 in a penalty shootout against Birkirkara to scrape into the Europa League third qualifying round.
West Ham United parted company with manager Sam Allardyce after the club's final Premier League match of the season.
Olivier Giroud scored for the fourth straight Premier League game and set up another goal in Arsenal's 3-0 win over West Ham on Saturday.
The FA says, Cole "admitted posting a comment on his Twitter account which was abusive and/or insulting and/or improper and/or brought the game into disrepute."
Eden Hazard scored the only goal as Chelsea beat West Ham 1-0 at Upton Park on Wednesday to maintain their five-point lead over Manchester City in the Premier League.
"West Ham United have been fined £30,000 after the club admitted an FA charge of failing to ensure its players cond
The former Real Madrid player had been training with West Ham and the 29-year-old was keen to revive his career back in England.
"I think we played very badly in the first half and we showed a lot of spirit in the second half, especially after the goal at the beginning," said Van Gaal.
Blind smashed home an injury-time equaliser to rescue a point for United against West Ham in a pulsating Premier League game at Upton Park on Sunday.