The new town of Lumumbaville would be a merger of two existing communities in central DR Congo, he added.
Mr Lumumba – a Soviet ally – was elected prime minister in 1960 after almost a century of colonial rule.
His killing some four months later at the age of 35 was widely blamed on US and UK intelligence agencies.
In April, UK House of Lords member Lord Lea said that former MI6 officer Daphne Park told him the UK had been involved in Mr Lumumba’s death.
‘Centre of Africa’
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He’ll want it to be a modern town with all facilities”
Raymond LumumbaLate leader’s son
The BBC’s Maud Jullien reports from DR Congo’s capital Kinshasa that the government’s decision is likely to be welcomed by most people, as he remains an extremely popular figure.
Lumumbaville will be built in Kassai-Oriental province, the birthplace of Mr Lumumba, to “honour the memory of a great Congolese statesman”, Mr Mende said.
Construction work would start in 2014, he added.
The government is hoping that Western donors will help finance the building of the town, and that it will become a major tourist attraction, our correspondent says.
Mr Lumumba’s son Raymond told BBC Focus on Africa his father would have welcomed the decision to build Lumumbaville.
“He wanted Congo to be the centre of Africa, the centre of development,” said Raymond Lumumba.
“So, he’ll want it to be a modern town with all facilities.”
DR Congo is rich in minerals but most people are extremely poor.
The country has been hit by numerous conflicts since it gained independence from Belgium in 1960.
The most recent uprising, by the M23 rebel group, began last year in eastern DR Congo, leading to some 800,000 people fleeing their home