He will return to Liverpool for treatment, but Hodgson is hopeful that he will be able to join up with the squad for Tuesday's trip to Ukraine in European qualifying Group H.
The once-capped Caulker, who signed a new four year deal with Tottenham in 2012, spent the 2011-12 season on loan to Swansea.
Ferdinand, 34, won the last of his 81 caps in a Euro 2012 qualifying match at home to Switzerland in June 2011.
An 88th-minute winner from substitute Edin Dzeko gave defending champions Manchester City a 2-1 win at home to Tottenham Hotspur on Sunday that took them up to second place in the Premier League.
Tottenham piled the pressure on Aston Villa manager Paul Lambert as the hosts swept to a stylish 2-0 win at White Hart Lane on Sunday.
England manager Roy Hodgson has warned his stars not to use the poor quality pitch in Chisinau as an excuse to deliver a lacklustre display in their opening World Cup qualifier against Moldova on Friday.
Chelsea captain John Terry was included in the England squad announced on Thursday for next month's World Cup qualifiers against Moldova and Ukraine despite facing disciplinary action for racial abuse.