Wyoming coach Larry Shyatt told ESPN on Monday that there was no structural damage to Martinez's broken hand and he won't require surgery.
Shyatt said it's premature to say how long Martinez will be out. He said Martinez is so tough that he would probably want to play immediately if he were allowed.
"He's been important to us," said Shyatt. "He's leading our team in scoring and steals and 3-point attempts and made, and second in 3-point percentage. He's an important person. He's very valuable and a great kid. Our guys have been very resilient all year. They have experienced enough. I trust them."
Martinez was involved in an off-campus incident, according to a statement from the school.
Shyatt wouldn't get into details about how Martinez was injured. When asked if Martinez was involved in a fracas of some sort, Shyatt declined to answer and referred to the statement that the university wouldn't offer any further details.
The undefeated Cowboys play at SMU on Wednesday before the Mountain West schedule starts.
ESPN.com senior college basketball reporter Andy Katz contributed to this report.