Warren, who recently dropped a similar case involving Tony Bellew, claims that Burns is still legally contracted to fight under his promotion.
"Since being promoted and managed by Frank Warren, Ricky Burns has earned just approaching three quarters of a million pounds and has had seven world title fights in just over two years," read a statement of Warren's website.
"Ricky Burns is under binding promotional and management contracts.
"Following the announcement by Eddie Hearn that Ricky Burns has signed with him, W. Promotions Limited and Frank Warren are suing Burns for substantial damages."
Burns is the current WBO lightweight champion.