The club confirmed that Martin would have scans on the same knee he injured last season, with a spokesman noting that the injury "did not look good".
Kurt Tippett and Ricky Henderson also left the field in the first half.
Callinan has suffered a detached right bicep muscle and will miss 10 to 12 weeks.
The news is better for Tippett, who will miss two weeks after hobbling off with an ankle injury sustained in a marking contest in the goalsquare in the first quarter.
Henderson's injury appeared more serious after a collision with Carlton defender Michael Jamison. He was stretchered from the field in a neck brace and play was held up for around five minutes, but later returned to the bench and is set to miss one week according to a club spokesman.
The injury to Tippett caps off a bad day for the Adelaide forward, who was in a minor car accident on the way to Adelaide Airport on Friday morning.
More to come
