The 29-year-old has served in the role since 2002 and was the first player to skipper the Blues following the transition to regional rugby in 2003.
"As I will not be available for the Blues until October due to my commitments with the Lions this summer, I feel it's in the club's best interest for me not to offer myself up for the captaincy this season," the 2005 Six Nations player of the championship told www.wru.co.uk.
"It has been a huge honour to be the first captain of the Blues and I have enjoyed every minute of it. I would like to thank all the players and fans for the support I have received over the last three years. I would also like to wish the best of luck to whoever takes over the captaincy next season - they have my full support."
Blues coach Dai Young said: "I fully understand and respect the decision Martyn has made. There's great morale in the squad at the Blues and we are totally united in focusing on what is best for the team.
"I think Martyn's decision reflects this and it is a great credit to him that he wants to put the squad's needs before his own. His decision this season will not rule him out from being the captain of the Blues sometime in the future and I would like to thank him for his loyal service over the last three years."