The Massachusetts Institute of Technology (MIT) says in a lawsuit that the Stata Center, completed at a cost of $300m in 2004, has persistent leaks.
It says snow and ice has fallen from window boxes and roofs, causing damage and blocking emergency exits.
Neither Mr Gehry nor MIT have commented on the case.
The suit, filed in Suffolk Superior Court in Boston on 31 October, seeks unspecified damages for costs and expenses incurred by the university.
It also alleges that the unconventional centre's outdoor amphitheatre began to crack due to drainage problems soon after it opened, and that mould grew on the centre's brick exterior.
The suit said Mr Gehry's firm, the Los Angeles-based Gehry Partners, "breached its duties by providing deficient design services and drawings".
The suit also names the construction company, New Jersey-based Beacon Skanska Construction Company, now known as Skanska USA Building Inc.
MIT paid Gehry Partners $15m to design the centre, which houses labs, offices, classrooms and meeting rooms.
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