The money was lent to Malaysian firm Weststar, which has agreed in principle to take over the company. The loan will have to be paid back in four weeks.
At the end of April, LDV, owned by Russian businessman Oleg Deripaska's GAZ group, announced the start of bankruptcy proceedings. The loan was announced shortly before the factory was due to go into administration.
"Weststar's proposed purchase of LDV offers the only credible chance of keeping this manufacturing plant in the U.K.," business minister Ian Pearson said.
"Whilst completion of the deal is not certain, it would have been irresponsible of the government not to support it going forward," he added. "But this is a one-off bridging loan and it cannot be extended."
Some 800 people are employed at LDV's Birmingham factory and around another 1,200 in its dealerships.
Tony Woodley, joint general secretary of trade union Unite, said: "We are delighted at the government's backing for this company."
"There's a long way to go yet but now thoughts can turn to building a serious and successful future for this company, and to getting these men and women, who have not built a vehicle in months, back to work," he added.
