Reuters could not independently confirm the report, and an aide to Strelkov declined to comment, saying: "No comments. I have clear instructions."
The ITAR-Tass news agency quoted another separatist leader as saying he could not rule out the report.
"I don't have specific information, but it is likely true," said Andrei Purgin, the DNR's deputy prime minister. "There is heavy fighting in that area."
A serious injury to one of the rebels' chief commanders would be a further blow to the separatists, who have abandoned a string of towns in eastern Ukraine to government forces in recent weeks. Kiev says rebel leaders, some of whom are Russian and who want union with Russia, are receiving arms from Moscow, an allegation the Kremlin denies.