The coal operations, employing 8,000 people, represent about one-tenth of Vattenfall's power production in Germany, where it is the third-largest energy supplier.
"The government supports the proposed transfer of Vattenfall's coal operations," said industry minister Mikael Damberg.
"Vattenfall is on the way to becoming a climate-neutral business," and is acting accordingly, Damberg told a press conference.
The deal is expected to close August 31st.
Climate activists had urged the government to block the sale, saying it should have shut down the heavily polluting German coal operations instead.
The approval paves the way for Vattenfall to sell its German lignite, or brown coal, business -- open-cast coal mines and two power plants close to the German-Polish border -- to Czech operator EPH.
Greenpeace Sweden slammed the deal, with local head Annika Jacobson telling Swedish news agency TT that "the lignite activities should instead be progressively abandoned in discussion with the German authorities."
The approval also drew fire from the Swedish Greens, who are part of the governing minority coalition along with the Social Democrats.
"The whole world is going to point at us and say that even a red and green government could not strike an agreement with the Germans to dismantle" the coal mines and power stations, said Carl Schlyter, a Green party lawmaker.
There is growing resistance to fossil fuels in Germany, where public subsidies of renewable sources of energy are making coal-fired energy less profitable.