WASHINGTON (AP) _ An underwater explosion tore open the hull of an American guided-missile frigate in the central Persian Gulf and injured 10 crewmen Thursday. Pentagon sources said it appeared the warship hit a mine.

The injured sailors - six with slight burns, one with second-degree burns, one with a hernia and two with back injuries - were evacuated from the USS Samuel B. Roberts, the Defense Department said.

The Roberts then began steaming slowly under its own power toward port in Bahrain.

The sailor with the second-degree burns was flown to Bahrain, the Pentagon said late Thursday. The other nine were transferred to the USS San Jose, a combat stores ship operating in the central gulf.

Defense sources said the crew of the Roberts had spotted ''some mine-like objects'' in the water immediately before the 10:10 a.m. EDT explosion. The Pentagon declined official comment on the report.

The sources, who insisted on anonymity, said the frigate was ''making only about two knots'' on its own power Thursday afternoon and would probably be taken under tow by the cruiser Wainwright.

The Roberts and Wainwright are two of 14 Navy ships assigned to the Persian Gulf force to provide protection to commercial ships flying the American flag. The San Jose was in the area only because it was on a resupply mission.

The Reagan administration increased the U.S. force in the region last summer in response to a request from Kuwait, whose oil tankers come under attack in the course of the Iran-Iraq war.

Dan Howard, the Defense Department's chief spokesman, said the Roberts had been in no danger of sinking and that the crew had managed to staunch flooding in the engine compartments on its own.

Howard refused to attribute the explosion to a mine, saying it was premature to form a judgment. ''Underwater explosion is the way to describe it. We don't know what caused the explosion,'' he told reporters.

However, other Pentagon officials were less reticent. ''The assumption is definitely that it was a mine,'' said one source.

According to Howard, the Roberts was steaming southbound on a routine patrol Thursday morning after completing a convoy operation the night before. The frigate, which had escorted the Kuwaiti tanker Gas King northward to Kuwait without incident, was almost dead center in the Persian Gulf when it was suffered the explosion - about 70 miles to the east of a navigational bell located off the coast of Bahrain.

The explosion ''caused flooding in the engine room and some hull damage,'' Howard said. ''The flooding is under control, and the ship is in the process of pumping out the water. It's operating under auxiliary power.''

The Roberts, whose home port is Newport, R.I., had left for Persian Gulf duty on Jan. 11 and was scheduled to leave the gulf for home around June 4, the Pentagon said.

According to Howard, the explosion occurred well to the south of the spot near the Iranian-controlled Farsi Island where a reflagged Kuwaiti tanker, the Bridgeton, hit a mine during the first of the Navy's convoy operation last July.

Howard said there had been no recent reports by mine sweepers in the area that mines had been sighted.

The last mine to be discovered in the gulf's waters was located on April 9 near Farsi, the Pentagon said. To date, 44 underwater mines have been destroyed by U.S. forces in the gulf.

The Roberts is the same type of guided-missile frigate as the USS Stark, the frigate that was hit last May in an Iraqi air attack. Thirty-seven crewmen died in that attack.

Ships of that class normally carry a crew of about 13 officers and 190 enlisted men. The Pentagon said the Roberts was carrying about 225 men, however, because it had a helicopter detachment aboard from Mayport, Fla..

At the White House, spokesman Marlin Fitzwater said President Reagan had been told of the incident, which he said ''only emphasizes our concern for stopping the Iran-Iraq war.''

Fitzwater said the administration intended to step up pressure in the U.N. Security Council for a resolution that would not only put an end to the war but put the group on record in favor of sanctions against belligerents in the war.