Zaur Gurtsiev, 34, received several medals for participating in Russia's gruelling assaults on the cities of Mariupol and Avdiivka.
Authorities did not say what caused the explosion, but also did not rule out that Ukraine was responsible.
A string of high-profile Russian servicemen have been killed in Russia since the Kremlin launched its full-scale military offensive on Ukraine in February 2022.
Videos posted by Russian Telegram channels showed two men, one of them Gurtsiev, positioned in a residential neighbourhood before a blast.
Kyiv has in some cases claimed responsibility or revelled in the attacks, calling them "legitimate targets" given Moscow's three-year offensive has killed tens of thousands.
"Our hero, veteran of the special military operation and participant in the Time of Heroes programme, Zaur Alexandrovich Gurtsiev, has died," said Stavropol region governor Vladimir Vladimirov, using Russia's term for its Ukraine offensive.
"All versions are being considered, including the organisation of a terrorist attack involving Nazis from Ukraine," he added, echoing the Kremlin's claim that it is fighting neo-Nazis in Ukraine.
The veteran's 29-year-old acquaintance died alongside him, Stavropol law enforcement said.
The Time of Heroes is the Kremlin's programme aimed to boost the careers of veterans stringently chosen to become part of Russia's future elite.
Gurtsiev was serving as Stavropol's deputy mayor.
He had commanded Moscow's air assault on the Ukrainian port city of Mariupol, a bustling Black Sea city devastated by Russian air strikes.
Russian forces rolled into Mariupol at the beginning of 2022 and imposed a brutal siege for nearly three months that resulted in 8,000 deaths, according to Human Rights Watch.
The siege included a deadly air strike on a theatre where civilians were hiding.
Ukraine does not typically comment on clandestine operations on the enemy's territory.
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