Green, whose presence in the side has not always attracted the universal approval of fans and pundits, will partner Stoke's Glenn Whelan in the centre of the field at Stockholm's Friends Arena.
Manager Trapattoni's team was otherwise as hinted at in training sessions this week, although the Italian, in naming his line-up, admitted a doubt over Hull City winger Robbie Brady.
Brady is not injured but Trapattoni wants to make sure he is mentally ready for the Group C encounter before finalising his side.
Millwall goalkeeper David Forde will make his first competitive start while Aston Villa's Ciaran Clark will partner John O'Shea in central defence.
West Brom striker Shane Long was selected alongside captain and record goalscorer Robbie Keane up front.
Trapattoni feels 29-year-old Green will offer more balance to his side than the attack-minded McCarthy as he looks to utilise the forward threat of players such as right-back Seamus Coleman.
Trapattoni said: "The situation is - away team, away game. I wish Coleman to go (forward). When he goes, we need protection.
"This result is very important and it is important we play our game.
"I saw his (Green's) last game in England. He he played very well.
"It is important we have protection in midfield. McCarthy also played very well but I couldn't ask him to stay in this position."
Trapattoni also challenged Brady, 21, to prove he is fired up for the contest.
He said: "I spoke with him. I said, 'Are you sure, are you okay?'
"He said, 'Yes'. I wish to push him. I liked him against Poland.
"I said he must repeat this game. He promised me after the training (he would) and I will speak again with him. It is not a big problem, only psychological. I push him.
"Against these strong teams character, technical (ability) and attitude are important."
Republic of Ireland team to face Sweden in World Cup Group C qualifier at Friends Arena, Stockholm: Forde, Coleman, O'Shea, Clark, Wilson, Brady, Green, Whelan, McClean, Keane, Long.