The Federal Trade Commission will investigate the purchase by Gamble-Skogmo Inc. of a major block of shares in Garfinckel, Brooks Brothers, Miller & Rhoads.

The FTC wants to assess the potential impact on retail competition of the cross ownership of the two big chain store companies, said Daniel Schuartz, deputy director of FTC's Bureau of Competition.

A Garfinckel spokesman said executives of that company were scheduled to meet today with FTC lawyers. A Gamble-Skogmo official in Minneapolis said the company had no comment on the FTC probe or other aspects of the stock purchase.

The FTC investigation was welcomed by Garfinckel executives, who are trying to protect the Washington company from being taken overy by Gambles.

In a lawsuit filed Wednesday seeking to force Gambles to sell the 12 percent of Garfinckel's stock which it purchased recently, Garfinckel charged that a merger of the two companies would violate anti-trust laws.

Schwartz confirmed reports that FTC would step into the case, noting that the agency recently has looked into several mergers and proposed mergers in the department store business.

The FTC, he said, is generally concerned about maintaining competition among big retail stores a field that is becoming increasingly dominated by chains and groups of affiliated companies.

An FTC investigation reportedly was a major factof in blocking a recent proposal by Carter-Hawley-Hale Inc., the Los Angeles company that owns Neiman-Marcus, to acquire Marshall Field, the big Chicago department store company.

FTC attorneys said the agency is concerned not only with the direct elimination of competition by merging two companies in the same business, but also with the indirect implications of connecting two potential competitors.

Garfinckel's lawsuit noted that the company and Gambles compete directly in the selling of large size women's clothing. The most recent addition to Garfinckel's retail family is Catherine's Stout Shoppes, the third largest retailed of so-called "half-size" women's apparel. Gamble-Skogmo own's Woman's World, the fourth largest business in that specialized field.

Both parent companies also have operations which sell moderate priced clothing to young women, but that line of business is bigger, more diversified and highly competitive.

Other aspects of the two firms' businesses are more diverse, with Gambles specializing in hard goods and mass merchandising and Garfinckel's stressing soft lines and premium prices.

But the links between the two big retailers could bring into play something FTC lawyers call "the wings effect."

When a company is part of a generalfield - such as retailing - but not involved in a specific segment of the market - such as shoe stores - it still contributes to competition because it is a potential competitor.

The potential competitors are considered to be "waiting in the wings" for their opportunity to enter the field. The combination of two broadly diversified retailers like Garfinckel and Gambles could eliminate "the wings effect" by cutting down on potential new areas of competition.

In another development yesterday, the head of the family which sold most of the Garfinckel stock acquired by Gambles said he had no quarrel with Garfinckel management.

Joseph R. Harris Sr. said he and his wife did not sell their "sizable number of Garfinckel shares. Harris, the founder of the Joseph R. Harris women's wear chain, sold the Washington business to Garfinckel's in 1971, acquiring in return about 10 percent of the stock of Garfinckel's. The stock was given by the elder Harris to members of his family, including his sons Joseph R. Harris Jr. and Donald Harris, who sold to Gambles.

"Members of my family have made it widely known for more than a year that they would sell their stock because of their desire to diversify their investments," said Joseph R. Harris Sr.

"I did not sell my shares to Gambles because my investment portfolio was acceptable to me," he explained. "I was pleased that I was able to take this action because of my friendship with Dave Waters (chairman of Garfinckel's) Bob Vandermark (executive vice president) and (Willard) Bud Bent (former chairman).

Harris stressed that there was no dispute within the family over the decision to sell the Garfinckel stock, which at market prices is valued at about $12 million.

Because of the size of the block of shares, the Harrises are believed to have received more than market prices, but neither the family nor Gambles has disclosed the price paid.