Japanese and U.S. authorities tonight were investigating the firing of three handmade rockets into the U.S. Embassy compound here this afternoon. No damage or injuries were reported in the attack, which appeared to be the work of members of Japan's extreme left.

Two other rockets were fired about the same time at the Imperial Palace of Emperor Hirohito, about a mile away. No injuries or damage was reported there, either.

The incidents caused new concern here over security for the Tokyo economic summit meeting scheduled for May, at which Prime Minister Yasuhiro Nakasone is to host President Reagan and other leaders of the industrialized world.

Japanese radicals, who form a tiny but highly committed minority in society here, have announced they will try to disrupt the summit and ceremonies marking the emperor's 60th year on the throne that are to be held next month.

There were no reports tonight that anyone had claimed responsibility for the attacks. There was no known connection to hostilities between the United States and Libya.

The rockets were made of tin cans attached to sticks about 12 inches long and launched automatically from stolen sedans parked on the street. The rockets whooshed out from the cars' trunks, which were opened by timing devices.

A leftist group known as the Middle Core Faction, at the forefront of a terrorist war against the new international airport at Narita, has frequently used similar weapons, which it apparently manufactures.

Last year, radicals fired similar rockets at the U.S. Consulate for Osaka and Kobe without causing damage or injury. The primitive rockets usually produce more panic and noise than damage.

Police this year have recorded 16 terrorist incidents in Japan. Late last year, leftist radicals paralyzed Tokyo for several hours by sabotaging its commuter rail system and stranding millions of people during the morning rush.