The outspoken official -- known for his Twitter spats with US billionaire and SpaceX CEO Elon Musk -- was removed from his position at Roscosmos in July.
Rogozin said on his Telegram channel Thursday that he suffered a back "injury" after a metal fragment was lodged above his right shoulder blade and will be needing surgery.
The incident took place on Wednesday evening in a hotel in Donetsk, where Rogozin was staying with a local official and a group of advisors, TASS news agency reported.
Russian investigators said that the strike, which had left others dead and injured, was carried out with "high-precision munitions, presumably... a Caesar" French artillery system.
Rogozin said the incident took place during a "work meeting" in the restaurant of the hotel, while Russian state news channel Rossiya 24 TV said the former space chief was celebrating his 59th birthday.
The channel broadcast images of the heavily damaged hotel and restaurant with parts of the roof destroyed and debris scattered around the rooms and outside in the garden.
Rogozin said he had regularly stayed in this hotel during trips to the Donetsk region, which Russia claimed to have annexed in September along with three other Ukrainian regions, despite widespread condemnation from the West.
"These are business trips by officials, it's quite normal for officials to go to Russian regions," Kremlin spokesman Dmitry Peskov told reporters when asked about the incident.
"Unfortunately, staying in some areas is still dangerous... but that does not mean that it should prevent officials from performing their duties," he added.