Glasnow is expected to make his first start for the Indians on Saturday night at Indianapolis' Victory Field against Charlotte.
"We are pleased with Tyler's development and believe he is ready for the next set of challenges in his career," said Pirates general manager Neal Huntington.
Glasnow is in line to make eight starts for the Indians, whose regular-season schedule ends on Labor Day, Sept. 7. Gerrit Cole made a total of 13 Triple-A starts prior to his mid-June 2013 big league debut.
Altoona manager Tom Prince has regularly been filling Bucs skipper Clint Hurdle's ears waxing about Glasnow's talents and progression.