Sprint said Dish's offer would leave non-tendering shareholders owning stock in a company "handicapped by unlawful corporate governance restrictions, onerous debt provisions, and potentially ... subject to massive money damages claims payable to Dish—an entity which has everything to gain from a failure of Clearwire."
The lawsuit also names Clearwire as a defendant.
Last week, Clearwire's board urged shareholders to accept the Dish tender offer, which values Clearwire at $4.40 per share. Sprint has offered $3.40 per share for the Clearwire stock it does not own.
Dish spokesman Bob Toevs said: "We are reviewing the complaint and considering our options."
Clearwire spokeswoman Susan Johnston said that company does not discuss pending litigation.
June 18 Deadline
The lawsuit adds a new complexity to a takeover battle in which SoftBank and Dish are bidding for Sprint, while Dish and Sprint are bidding for Clearwire.
(Watch: Sprint& SoftBank Reach Deal With US
Last week, SoftBank raised its offer for Sprint to $21.6 billion from $20.1 billion, which would give it a 78 percent stake in the Overland Park, Kan.-based company.
The new offer includes $16.6 billion of cash, and would be the largest overseas acquisition by a Japanese company.
Sprint then gave Dish, a satellite TV provider controlled by billionaire Charlie Ergen, until June 18 to sweeten the $25.5 billion bid, which it said is not "actionable," and make its best and final offer.
Dish is based in Englewood, Colo., and Clearwire in Bellevue, Wash.
Known for pursuing fierce takeover battles, Ergen is interested in Clearwire to expand into wireless amid a maturing of Dish's traditional pay-TV business.
Sprint, meanwhile, hopes to use Clearwire to help it better compete in mobile communications with larger rivals AT&T and Verizon Wireless.
SoftBank had approved the Sprint bid for Clearwire, but said it would be content even if shareholders rejected that bid because Sprint would still control a majority of the company.
The Japanese company is controlled by billionaire founder Masayoshi Son, who is known as a risk-taker despite his country's normally cautious corporate culture.
Shareholders of Sprint are scheduled to vote on the $21.6 billion SoftBank offer on June 25.
Paulson & Co., the hedge fund firm run by billionaire John Paulson and Sprint's second-largest shareholder, has said it would vote for the SoftBank transaction.
(Read More: Hedge Fund Billionaire Paulson Glosses Over His Losses)
The lawsuit was announced after U.S. markets closed. In Monday trading, Sprint shares closed down 10 cents at $7.22, while Clearwire shares were unchanged at $4.63.
The case is Sprint Nextel Corp et al v. Dish Network Corp et al, Delaware Chancery Court.