This is well short of the government's more upbeat projection as weaker global metal prices weigh on expansion, the World Bank said on Wednesday.
Finance Minister Patrick Chinamasa said last month the economy was expected to grow by 6.4 per cent in 2014 up from 3.4 per cent last year, buoyed by mining, agriculture and construction.
But Nadia Piffaretti, the World Bank's senior country economist for Zimbabwe, told a forum in Harare that mining could be hit by softening metal prices and subdued investment.
"Amidst uncertainty around mineral prices and recovery in the agricultural sector, the baseline projections forecast economic growth at 4.2 per cent in 2014," she said.
Agriculture is critical for the livelihood of a majority of Zimbabweans, since 80 percent of the working-age population do not hold a formal job.
A million people in rural Zimbabwe benefiting from United Nations World Food Programme (WFP) aid are also facing hunger as a lack of funding has caused deep cuts in assistance.
Piffaretti said 46 per cent of Zimbabwe's 13 million people now ran an informal business. This would likely include those hawking everything from mobile phone recharge cards to vegetables on the streets.