Russian media said he was being treated at Moscow’s Central Clinical Hospital and died of his injuries.
Maganov is the latest of a number of high-profile business executives to die in mysterious circumstances.
Investigating authorities said they were working at the scene to establish how he died. Tass news agency quoted sources saying he had fallen out of a sixth-floor window early on Thursday morning, adding later that he had taken his own life.
Shortly after Russia invaded Ukraine, the Lukoil board called for the conflict to end as soon as possible, expressing its sympathy to victims of “this tragedy”.
Its billionaire president, Vagit Alekperov, resigned in April after the UK imposed sanctions on him in response to the invasion.
Several Russian energy oligarchs have died in unusual circumstances in recent months:
The body of millionaire Novatek former manager Sergei Protosenya was found alongside his wife and daughter at a Spanish villa in April
A former vice-president of Gazprombank, Vladislav Avayev, was found dead with his wife and daughter in their Moscow flat, also in April
In May, a former Lukoil tycoon Alexander Subbotin died of heart failure, reportedly after seeking alternative treatment from a shaman.
Lukoil is Russia’s biggest private company. In its statement it said it was down to Maganov’s managerial talent that it had evolved into one of the world’s largest energy firms.
He began working for the private oil company in 1993 and took over as chairman two years ago. Three years ago he was given a lifetime achievement award by President Vladimir Putin.
Maganov had been receiving treatment at a hospital on the western outskirts of Moscow, which is known for having Russia’s political and business elite among its patients.
Mikhail Gorbachev died at the same hospital, Central Clinical Hospital, on Tuesday and President Putin visited the site on Thursday morning to lay flowers beside his coffin.