The franchise tag would have cost the Ravens $11.654 million. The transition tag would have cost $10.039 million.
Monroe is now scheduled to become an unrestricted free agent by March 11 at 4 p.m. when the free agency signing period launches.
Other NFL teams can now legally talk to Monroe by Friday, but can not sign him to a contract.
The Ravens remain far apart in contract negotiations with Monroe, according to sources.
He's their top negotiating priority.
The highest-graded offensive lineman on the team last season, Monroe, 26, is regarded as being in the prime of his career and is expected to be heavily pursued if he hits free agency.