The 38-year-old made 40 appearances this season as the Edinburgh side finished third in the Premiership.
But Hearts' website states that, with European football in mind, boss Robbie Neilson "believes the time is now right to start building for the future".
"We'll now look to bring in another goalkeeper as part of our summer recruitment," said head coach Neilson.
Alexander joined Hearts as player-coach after leaving Crystal Palace in June 2014 and has made 72 appearances in two seasons.
Neilson thanked him for his role in helping Hearts win the Championship title and promotion last season and secure a place in the Europa League qualifying rounds in their first season back in the top flight.
Alexander, who began his career with Stenhousemuir and also had spells with Livingston, Cardiff City, Ipswich Town and Rangers, won three caps for Scotland.
His back-up at Hearts has been Scotland Under-21 international Jack Hamilton, now 22, while 17-year-old Kelby Mason is the other goalkeeper on the books at Tynecastle.
Meanwhile, Hearts midfielder Perry Kitchen has been named in the United States squad for their friendly against Puerto Rico on 22 May.
Kitchen is pushing for inclusion in Jurgen Klinsmann's final 23-man squad for the Copa America.
Veteran goalkeeper Neil Alexander is being released by Hearts despite spending the season as first choice.