Martin played a role in the Tigers' second-quarter fightback at the MCG on Sunday but suffered the fresh injury concern early in the third term and had to be substituted out of the game.
The 33-year-old finished with just seven disposals in the 20.11 (131) to 10.10 (70) defeat - the lowest tally of his 301-game career.
"He just seized up," Yze said.
"He tried to go back out there for one more rotation and he was just battling, so it was just pointless.
"I'm not sure if he's ever been subbed before but against a quality team like Carlton you need 18 fit guys out there.
"So for him to put his hand up and say his back's a bit too sore is a credit to him."
Yze had already flagged resting Martin on return from the mid-season bye, with Richmond wary of short breaks leading into interstate clashes with Fremantle and Port Adelaide over the next three weeks.
Martin will be given a day off before returning to Punt Road on Tuesday for further assessment ahead of the Dockers clash at Optus Stadium on Saturday night.
"Whether this is a reason why he needs to miss because he's got a tight back now - our hand might be dealt anyway," Yze said.
"If he bounces out of the game OK, there's no reason why he can't play against Freo.
"We've just got to have those discussions and think about it more than anything."
Martin battled calf problems earlier in the season and Yze said the latest setback was a "random" one.
"He probably copped a knee out there, which he wouldn't have known," Yze said.
"He's a combative player and he actually helped us at centre bounce in the second quarter, so we did miss him in the second half when he went out of the game.
"Hopefully he's OK."
Richmond have used 41 players this season - more than any other club - amid a raft of injuries, including many to key players.
Premiership midfielder Dion Prestia (calf) could return against Fremantle, but Tom Lynch (hamstring) is unlikely.
Yze was full of praise for mid-season draftee Jacob Blight, who made his debut against Carlton and helped limit star forward Harry McKay's influence.
"Blighty held up his own as one of the best in the competition and he will be better for it," Yze said.
"He did well, the young kid."
