Robert Molenaar will be asked to play through the pain in City's FA Cup tie at West Brom on Saturday.
The Dutch centre-half is set to return at the Hawthorns as Peter Atherton sits out a one-game ban.
Molenaar, pictured, has been struggling with a badly-swollen ankle which forced him to miss the win at Wolves. He would not have played yesterday (New Year's Day) if the Grimsby game had gone ahead.
Referee Mark Clattenburg gave City's relegation clash as long as possible and held two inspections of the waterlogged Blundell Park pitch. But a further downpour in the morning following constant rain the previous day ruled out any chance of playing and the official called it off at midday.
It is the second year running that the weather has left the Bantams kicking their heels on New Year's Day. Last season, the derby visit to Burnley was postponed because of ice.
Boss Nicky Law was frustrated that his team did not have the chance to build on their back-to-back victories although the Grimsby cancellation will give Molenaar more recovery time.
Law said: "Robert wouldn't have made it and I think he will be touch and go for the weekend. But with Pete suspended it might have to be a case of strapping Robert up and getting him ready for action."
Law was waiting to be picked up by the team coach on the way to Grimsby when he got a call from chairman Gordon Gibb to say the game was off.
He added: "It was a big disappointment because we had a bit of momentum going over the last couple of games. We were on a good run and wanted to keep that going.
"A postponement probably suited Grimsby a bit more than it did us."
Relegation rivals Brighton were also washed out but Stoke and Sheffield Wednesday took the chance to steal a march on the pack at the bottom with crucial wins.
Wednesday beat neighbours Rotherham 2-0 at Millmoor and Stoke, after 16 games without a win, made it two in two with a 2-1 victory over plummeting Preston.
Stoke's win reduces City's cushion from the side third from bottom to five points but they have a game in hand.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article