According to sources, Martin was the subject of some ribbing on Monday and was angry about it. One source said Martin's fellow offensive linemen were behind the incident, and it happened in the Dolphins' lunch room.
"O-line made fun of him and he snapped," a source said.
Martin left the team this week and has been declared out for Thursday night's game against the Cincinnati Bengals due to an illness. Neither source was sure when Martin would return.
Backup right tackle Tyson Clabo will start in Martin's place vs. the Bengals.
Martin, a former Stanford product, was a 2012 second-round pick of the Dolphins. He has started every game for Miami this season. He spent the first six games at left tackle and one at right tackle.
According to Fox Sports 1, which had earlier reported the news on Wednesday evening, Martin is with his family and receiving treatment.
A person familiar with the situation told The Associated Press that Martin is receiving professional assistance for emotional issues. The person said Thursday that Martin was with relatives, and that his issues didn't involve any problems with the coaching staff.
The Dolphins have not announced any details of Martin's illness. Martin's agent didn't respond to requests for comment.
Information from The Associated Press contributed to this report.