Tokyo District Court approved the arrest warrants within hours of a police request, Kyodo News Agency said. Neither the court nor the Tokyo Metropolitan Police Department could immediately confirm the report.
The aim of the warrants was to place the two Americans, ages 41 and 30, and a 28-year-old Briton on an international wanted list, Kyodo said.
The three activists have not been named.
"Regardless of a difference of opinion, it is unacceptable that those who are involved (in whaling) get injured ... or face life-threatening dangers. It is to my understanding that the international community will agree on our position," Chief Cabinet Secretary Nobutaka Machimura said Monday at a routine news conference.
"Opposing the research is one thing but physical threats against whaling ships must be restrained," Machimura said.
Sea Shepherd's activists aim to disrupt Japan's annual whaling operations through high-seas confrontations with their own boats.
In February 2007, the anti-whaling group's boat and a Japanese whaling vessel collided twice in Antarctic waters during clashes near a pod of whales. Around the same time, Sea Shepherd activists also dumped a foul-smelling acid made from rancid butter on another whaling ship, slightly injuring two crew members and prompting Japanese officials to label them "terrorists."
Japan kills about 1,000 whales a year under a scientific whaling program that Tokyo says provides crucial data for the International Whaling Commission on populations, feeding habits and distribution of the mammals in the seas near Antarctica.
The hunts are allowed by the International Whaling Commission, but the Sea Shepherd and environmental groups have long condemned the hunts as a pretext for keeping commercial whaling alive after the practice was banned by the commission in 1986.
The Japanese have hunted whales for centuries, and whale meat was widely eaten in the lean years after World War II. However, it has plunged in popularity in today's prosperous Japan. While still on the menu in a few upscale Tokyo restaurants, the meat is only eaten regularly in small coastal communities.
Sea Shepherd could not immediately be reached for comment, but the group says it tries to avoid any physical injury to whalers.
In June, the group announced plans to try to disrupt Japan's 2008-09 whaling season in the Antarctic.