A Navy ship headed toward an exercise in the Indian Ocean was delayed for 11 days last fall when its civilian captain and deck officers went on strike, Navy officials confirmed last week.

The tanker, SS Mormac Star, is one of a growing number of ships owned or leased by the Navy but operated by civilian crews. Nine other Navy ships were affected when the International Organization of Masters, Mates and Pilots called a strike Oct. 3, although none was delayed as long as the Mormac Star, Navy Lt. Dave Morris said in response to a question.

The unusual strike, which the Navy did not publicize at the time, calls attention to the Navy's growing dependence on civilian crews as the fleet expands toward the Reagan administration's goal of a 600-ship force. Civilians now man 123 Navy ships, up from 78 four years ago. These include supply, repair and submarine-tracking vessels.

"We have a limited field of people to operate our ships," Everett Pyatt, assistant secretary of the Navy for shipbuilding and logistics, told a congressional subcommittee last year. "In looking at the availability of people and the requirements for people, we believe that it is important to first of all fully man all the combatants and auxiliaries in the Navy."

The Navy said that civilian crews on submarine-trackers would not present problems in wartime.

"There is no contingency plan to replace civilian crews and technicians with military personnel, nor is one deemed necessary," the Navy said in response to a question from the House Appropriations subcommittee on defense. "The U.S. merchant marine has a long, honorable reputation for service to this country in war."

The Navy's Military Sealift Command controls the 123 ships and hires Civil Service crews to operate about half of them. The other half are operated by private shipping lines, which generally hire union crews.

The Mormac Star, for example, is owned by the Moore McCormack Bulk Transport Lines of Stamford, Conn., and is leased to the Navy to deliver fresh water to an Indian Ocean flotilla that carries "pre-positioned" weapons and equipment for the Rapid Deployment Force.

Last October, when the ship was supposed to set sail from the naval base on the tiny Indian Ocean island of Diego Garcia, three unions represented different members of the crew: the Masters, Mates and Pilots union, for deck officers; the Marine Engineers Beneficial Association, for engineers, and the National Maritime Union, for seamen.

Moore McCormack and four other shipping lines had declined to renew their contracts with the deck officers' union, however, and the union responded with a strike.

"They did agree to maintain the security of the ship," said a company official who asked not to be identified. "However, when asked by the Navy to make a scheduled sailing, they refused to take the ship out."

Burton M. Epstein, general counsel for the 12,000-member Masters union in Linthicum, Md., said: "It was the action of the company which precipitated the incident. If you're told . . . you're no longer members of the pension plan, that your wages are reduced, [then] you can choose to continue working or you can ask to be relieved."

The company sent a replacement crew to the base, but the striking deck officers prevailed upon the new arrivals to join the strike, the company official said. By the time a second crew could reach the island, 11 days had passed.

Nine other ships affected by the strike found replacement crews soon enough to meet their sailing dates, or met their schedules by steaming faster than planned after leaving port, Morris said. Most of the vessels were transport oilers.

The Navy is building a dozen submarine-tracking ships that will be manned by union seamen and contract technicians. The $39 million price tag on the ships includes an extra $1.75 million for each, "to incorporate single-man staterooms," as union crews demand, the Navy said.

The unions contend that they operate such ships more cheaply because they use fewer sailors than the Navy and because of the high retirement costs for Navy sailors.

Rep. Jack Hightower (D-Tex.), a subcommittee member, expressed concern about putting nonmilitary crews on submarine-tracking ships.

"We never know when they might be in combat," Hightower pointed out during a hearing last year. "Contract seamen might very well say upon the initiation of hostilities, 'That is not in my contract, take me home,' and they could sure do it, could they not?"

"One of the provisions in the contracts is that they will stay there," Pyatt replied.