Barry hurt himself when he fell over a team-mate during the second half of the 1-0 defeat that ended City's hopes of qualifying for next season's Champions League.
The former Aston Villa man has already been ruled out of Sunday's trip to West Ham.
England coach Fabio Capello will be interested to know the results of the scan given Barry is a certainty for his 23-man World Cup squad.
Capello will name his 30-man provisional squad for South Africa on Tuesday and will not want any doubts over a player who is regarded as a first-choice member of his starting line-up, having struck up an impressive midfield partnership with Frank Lampard.
City manager Roberto Mancini claimed last night that the damage was "not too serious" although he admitted he it would require further tests for a full diagnosis to be confirmed.
If the injury is similar to the one Wayne Rooney suffered against Bayern Munich last month, Capello will be relieved.
Although Rooney did not look fit when he returned to action for the second leg a week later, England are not due to depart for the first of two training camps in Austria until May 17, are not scheduled to play until fellow finalists Mexico visit Wembley on May 24 and do not begin their World Cup quest for over five weeks, tackling the United States in Rustenburg on June 12.