Eastman joins Mark Kennedy, centre-half Gareth McAuley and midfielder Luke Hyam on the treatment table.
"Tommy has a groin injury and at this stage he has to be doubtful for the Norwich game," manager Roy Keane told the club's website.
Eastman, a Town youth product, has made 12 Ipswich appearances this season, after featuring just once in the last campaign.
I have to say, I am DREADING watching this one. I'll be watching through the gaps in my fingers with my hands over my eyes for the most part
HampshireYorkshireIpswich...
A torn hamstring is likely to keep 19-year-old Hyam out for another four weeks, while veteran left-back Kennedy's own hamstring problem will not see him return for another fortnight.
McAuley, 30, could shake off an Achilles injury in time to face the Canaries on Sunday.
Keane was boosted by the return of captain David Norris and on-loan Celtic defender Darren O'Dea to his side for the 1-0 reverse at Hull.
But Town's reliance on youngsters continued with 10 of their 18-man squad against the Tigers aged 23 or under.
Source: BBC Sport
Source: BBC Sport