Slovak media said the shooter was a 71-year-old man but the motive was not immediately clear.
Fico is still undergoing surgery and is in an extremely serious condition, Defence Minister Robert Kalinak told reporters on Wednesday.
Slovak Interior Minister Matus Sutaj Estok said authorities suspected the attack was politically motivated.
Slovakia, a member of NATO and the European Union, has little history of political violence.
Russia's President Vladimir Putin and US President Joe Biden joined Slovakia's EU partners in expressing shock and condemnation of the shooting.
Fico, 59, was rushed to hospital in the central Slovak town of Handlova where he had been chairing a government meeting.
He was then transported by helicopter to regional capital Banska Bystrica for urgent treatment, it said, adding that his condition was too serious for him to be taken to Bratislava.
A Reuters witness heard three or four shots as Fico exited a building to shake hands with a crowd of people who had been waiting to greet him.
Police then wrestled a man to the ground.
"An assassination (attempt) on Prime Minister Robert Fico was carried out today at the government's off-site meeting in Handlova," the government office said in a statement.
Prime Minister Robert Fico spoke with people before a cabinet meeting in the town of Handlova. (AP PHOTO)
Slovak news media reported the shooter was a former security guard at a shopping mall, an author of three collections of poetry and a member of the Slovak Society of Writers.
Atkuality.sk cited his son as saying his father was the legal holder of a gun licence.
"I have absolutely no idea what my father intended, what he planned, what happened," news outlet Aktuality.sk quoted the shooter's son as saying.
Broadcaster TA3 reported four shots had been fired, and that the progressive populist prime minister had been hit in the abdomen.
"I don't think I will wake up from this," Lubica Valkova, a 66-year-old resident told reporters.
"This kind of thing just can't happen in Slovakia."
Fico, who returned as prime minister last October for the fourth time, has drawn criticism in some quarters for taking a more pro-Russian stance in the Ukraine war and initiating reforms of criminal law and the media which have raised concerns over the rule of law and prompted street protests.
Describing the shooting as a "monstrous" crime, Putin said in a telegram sent to Slovakia's President Zuzana Caputova: "I know Robert Fico as a courageous and strong-minded man. I very much hope that these qualities will help him to survive this difficult situation."
Caputova said the attack on Fico was shocking.
Utterly shocked by today's brutal attack on — Zuzana Čaputová (@ZuzanaCaputova) #Slovakia's Prime Minister Robert Fico, which I condemn in strongest possible terms. I wish him lot of strength in this critical moment and early recovery. My thoughts are also with his family and close ones.May 15, 2024
Biden offered US help to Slovakia, saying in a statement: "We condemn this horrific act of violence."
Fico's close ally Lubos Blaha, deputy parliament speaker and deputy chairman of the prime minister's SMER-SSD party, blamed what he called the "liberal media" and opposition for creating an atmosphere that led to the shooting.
"For SMER-SSD, I want to sharply condemn what happened today in Handlova and at the same time express heavy disgust over what you have committed here in the past years," Blaha said.
"You, liberal media and political opposition. What hatred you spread against Robert Fico."
Slovakia's biggest opposition party Progressive Slovakia called off a planned protest against government public broadcaster reforms set for Wednesday evening.
"We call on all politicians to refrain from any expressions and steps that could contribute to an escalation of tension," said Michal Simecka, leader of Progressive Slovakia, a pro-EU party.
During a three-decade career, Fico has moved between the pro-European mainstream and nationalistic positions opposed to EU and US policies.
He has also shown a willingness to change course depending on public opinion or changed political realities.
Fico has grown increasingly critical of military support for Ukraine in its war with invading Russian forces and has expressed opposition to allowing Ukraine to join NATO in the future.
Ursula von der Leyen, President of the European Commission, condemned what she described as a vile attack on Fico.
