Stranzl quits Austria national team
The Spartak Moscow player won 56 caps, scoring three goals, between 2000-09.
Constantini, who has also caused controversy by refusing to call up German-based midfielder Andreas Ivanschitz, said he accepted the decision.
"I respect Martin Stranzl's decision and accept his retirement," he said on the Austrian federation's website.
"I wish him lots of success in his career."