The 33-year-old is ineligible to play at Goodison Park due to rules involving his loan agreement from the Etihad Stadium.
"It's a fixture I looked at earlier on in the season because the last home game of the season is always a special one," Barry told the club's official website.
"You want to be out there in front of your home fans for the last time that season, especially when there is something at stake as well."
Barry, who moved to the Merseyside outfit from City last summer, is expected to return for Everton's last game of the season against Hull City on May 11.
The Toffees are currently four points behind Arsenal, who occupy the final Champions League spot.