The Manchester City captain has been riddled with injury problems over the last few seasons.
The 32-year-old has been selected as part of the Red Devils' 23-man squad despite suffering an injury scare at the weekend.
The centre-back appeared to pick up a groin problem during Belgium's goalless draw with Portugal on Saturday.
Martinez has since explained why Kompany has been included, adding that he is crucial to the squad.
"The situation is clear. We will try to use the rules to our advantage - we have to make the final outfield squad 24 hours before our game against Panama on June 17," Martinez told reporters.
"We will try to give the maximum reaction time to see what the problem is with Vinnie. For any player, a scan would reveal the extent of the problem but with Vincent, we spoke closely with Man City and the experience over the past few years shows that his reaction to certain soft tissue injuries cannot be described via a scan.
"We will wait for a period of seven or eight days and then get a good opportunity to make a good diagnosis. The approach is very easy. Vincent has been a leader, working extremely hard in the camp for the Red Devils. He performed in a fantastic manner on the pitch against Portugal.
"A fresh performance and his leadership is essential for us. It's a World Cup - not just any competition - and due to the role of Vinnie, it's a decision we've taken in order to give the best possible chance to make the right decision."
Kompany has earned 77 caps for his country.