Doctors said the condition of Sharon, 77, was stable and not life-threatening, although they expect him to stay in hospital for three or four days.
"I feel fine," Sharon was quoted as saying by aides. Israeli television said he had told doctors: "You're not getting
rid of me yet."
Shmuel Shapira, a doctor at Hadassah Hospital, where Sharon was admitted on Sunday, told Channel 1 television: "The prime minister is conscious. He is undergoing tests. His condition is stable."
Another medical worker said earlier: "He lost consciousness on the way to hospital and then regained it."
Aljazeera's bureau chief in Ram Allah said that Sharon felt unwell after a meeting with Shimon Peres at his office in Jerusalem.
On his way home, while talking on the telephone to his family, Sharon asked his guards to take him to hospital, where he underwent a brain scan.
Ariel Sharon's son, Omri, (R)
arrives at Hadassah Hospital
Raanan Gissin, Sharon's spokesman, said there was no question of anyone standing in for the prime minister, even temporarily.
"He is fully lucid, in full control," Gissin said.
Ehud Olmert, the vice prime minister, would assume Sharon's duties in the event of his disability or death.
Although Sharon has had no previous health scares, he has occasionally appeared drawn recently as he has struggled to push through an Israeli pullout from the Gaza Strip, which was completed in September.
Israeli television reports said he had suffered a minor stroke, a condition caused by sudden blockage of blood to the brain.
Doctors usually have a three-hour window in which to administer a drug, called TPA, to try to dissolve a blood clot.
"He is fully conscious and is undergoing a series of tests"
spokeswoman for Hadassah Hospital
Yael Bossem-Levy, a spokeswoman for Hadassah Hospital, said: "He is fully conscious and is undergoing a series of tests." She would not give additional details.
Minor strokes can cause temporary weakness or numbness in arms and legs, as well as speech difficulties.
Sharon is in the midst of a campaign to win re-election in a national vote on 28 March.
He leads a centrist movement that he established last month after quitting the Likud party in the face of a far-right rebellion over the Gaza withdrawal.