The Washington Post Co. and CBS Inc. announced yesterday that they have agreed to sell their partnership interests in SportsChannel cable networks to a wholly owned subsidiary of Cablevision Systems Corp., the third partner in the four regional cable sports services.

The Post company transaction, which is expected to be completed by the end of 1987, will produce a total after-tax gain for the publishing and broadcasting company of approximately $6 million.

Neither the Post company nor CBS would disclose terms of the agreement.

Cablevision Systems Corp. of Woodbury, N.Y., said the two transactions will have an approximate value of $56.2 million and are expected to close by the end of the year.

Washington Post Co. President Richard D. Simmons said that the company decided to sell its interest in the enterprise because delays in installing cables in New York and other cities made it "clear that the investment is not producing for our company the financial returns we anticipated when we entered the business in 1983."

Installation delays in New York City, where cable is not widely available outside of Manhattan, have caused hardships for SportsChannel. SportsChannel, which has more than 2 million subscribers, has not gotten the number of subscribers needed to produce the returns projected, according to Post company spokesman Guyon Knight.

The Post company is selling one-third interests in SportsChannel Associates in New York, SportsChannel Prism Associates in Philadelphia and SportsChannel Chicago Associates, and its one-sixth interest in SportsChannel New England.