The state Investigative Committee said the writer's Audi Q7 was blown up in a village in the Nizny Novgorod region, about 250 miles (400km) east of Moscow, which it was treating as an act of terrorism. It said Prilepin had been taken to hospital.
The committee released a photograph showing the white vehicle lying overturned on a track next to a wood, with a deep crater beside it and fragments of metal strewn nearby.
An interior ministry spokeswoman said a suspect had been arrested. State news agency TASS quoted security sources suggesting the suspect was a "native of Ukraine" with a past conviction for robbery with violence.
Interfax news agency quoted a source in the emergency services as saying Prilepin's condition was serious and doctors would operate on him.
The novelist is an outspoken champion of Russia's war in Ukraine and has boasted of taking part in military combat there. He was the third prominent pro-war figure to be targeted by a bomb since Moscow's full-scale invasion of its neighbour in February 2022.
Russia has blamed Ukraine for the deaths of journalist Darya Dugina and war blogger Vladlen Tatarsky in the two previous attacks. Kyiv has denied involvement.
Ukrainian presidential adviser Mykhailo Podolyak posted a cryptic comment on Twitter about Saturday's incident, appearing to suggest it was the result of Russian infighting.
Russian Foreign Ministry spokeswoman Maria Zakharova wrote on Telegram: "The fact has come true: Washington and Nato fed another international terrorist cell – the Kyiv regime."
She claimed it was the "direct responsibility of the US and Britain", but offered no evidence whatsoever for what has been a regular complaint of Moscow – the support by Western allies of Ukraine for their fight against Russia’s invasion.
Officials at the White House, Pentagon and State Department did not immediately respond to requests for comment. No comment was immediately available from the UK Foreign Office.
It was the second time this week that Moscow has accused Ukraine of carrying out terrorist attacks on behalf of the West, a narrative it appears to be pushing with increasing urgency.
On Wednesday, Russia accused Ukraine of trying to kill President Vladimir Putin with a night-time drone attack on the Kremlin. Ukraine denied that too, and the White House said accusations that Washington had a hand in it were "lies".
TASS quoted Kremlin spokesman Dmitry Peskov as declining to comment on Saturday's car bomb in the absence of information from investigators. The agency said former Russian president Dmitry Medvedev had sent a telegram to Prilepin, calling the incident "a vile attack by Nazi extremists".
Mr Prilepin often speaks out in support of the Ukraine war on social media, with more than 300,000 followers on Telegram and his own website and YouTube channel.
He fought for Russian proxy forces in eastern Ukraine before last year's invasion and led a military unit there, boasting in a 2019 YouTube interview that his unit "killed people in big numbers".
"These people are dead, they are buried and there are many of them," he said. "Not a single unit among the Donetsk battalions had such results. It was outrageous chaos what we did there... Not a single field commander had such results as I had."
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