Lampard picked up the knock last week but remained hopeful of playing against the minnows at Wembley on Friday night.
Fellow Chelsea player Ryan Bertrand, a late call-up to the squad, has also returned to the Blues after it was reported he had a sore throat. But the left-back insists it is more serious.
He tweeted: 'Just to clarify.... Its not a "sore throat" I'm ill. Swollen glands in my neck... And constant headache for 3 days now and freezin cold.'
Bertrand is also due to rejoin the squad on Sunday.
Lampard's absence means manager Roy Hodgson will have to decide on a new captain for the San Marino match.
Regular skipper Steven Gerrard sits out through suspension and Lampard was next in line.
His absence opens the door for someone else with Manchester City goalkeeper Joe Hart reportedly in the frame.
In contention: Joe Hart has been touted as a candidate for the armband
'I've no idea who is going to be captain but I am pretty sure it will fall to Rooney,' said Hart.
'He is our star man with 10 million caps at the age of whatever he is, 26? I imagine he is a little bit further up the queue than me.'