Defence Minister Shaul Mofaz ordered their detention after receiving intelligence information about their alleged involvement in "violent ideological activities against Arabs," a ministry spokeswoman said on Sunday.
Israeli media said the three were members of the outlawed anti-Arab Kach movement and that they were detained at the funeral of Eden Nathan Zaada, a 19-year-old army deserter who gunned down four Israeli Arabs on a bus on Thursday.
The shooting marked the deadliest attack by a Jewish militant in more than a decade. The gunman was beaten to death by enraged residents after the attack.
Israel has in recent months detained several other rightists, including Kach members, who engaged in violent protests against Israel's planned pullout from the Gaza Strip, the first withdrawal from the land Palestinians want for a state.