The three patients going to Germany, two residents of Volgograd and a third from Kazan, received burns on 60 to 70 percent of their bodies, RIA-Novosti reported.
Doctors say their injuries are not limited to external burns, but include serious damage to internal organs, especially the kidneys.
Volgograd's City Hall ordered the purchase of two artificial kidney units at a price of 4 million rubles ($133,000) to treat the three most critical patients, still in a city treatment center.
The 10 patients sent to Moscow are listed in critical condition but are stable, with burns covering 30 to 60 percent of their bodies.
On the evening of Feb. 14, a gas cylinder intended for heating ruptured and exploded at the Italian cafe Bellagio, injuring 23. Temperatures in the region have been extremely low in the region, prompting the restaurant management to purchase two new gas heaters.
Security cameras show patrons of the restaurant fleeing out a window to escape flames and smoke billowing from the first-floor restaurant.
The owner of the cafe, who was questioned about the explosion and ordered not to leave the city, has offered to pay for the medical treatment of one of the victims in Germany.
He may face criminal charges under two articles of the Criminal Code: provision of services that do not meet safety requirements resulting in grievous bodily harm and violation of fire safety requirements. The maximum penalty for these charges is up to six years in prison.
The cafe was closed for 30 days in December 2010 after an inspection revealed numerous safety violations. A second check was made with no violations reported, and a repeat check in December 2011 also found no violations.