Wright was first called up by England last summer, and has played in five one-day internationals and seven Twenty20 internationals.
Like Mascarenhas, he is not centrally contracted by the England & Wales Cricket Board (ECB), so he would only have needed the permission of his county to play.
He and Bopara will now line up for the England Lions side against the New Zealand tourists in a four-day match which begins at Southampton on Thursday.
Wright added: "Obviously I was very pleased to be considered for the IPL.
"If the timings were different and it wasn't going to affect my chances of playing for England then it would be something I would seriously have to consider.
"I am now very much looking forward to the match against New Zealand which is obviously a great chance for me to prove myself in the longer version of the game and hopefully push for a Test place."
Bopara has played in 21 ODIs but was dropped from the Test team after the three-match series in Sri Lanka during the winter - while Mahmood has not been picked for England since their unsuccessful World Cup campaign in the spring of 2007.
