Samuel Undenge, 62, will serve just two-and-half years after 18 months were suspended on condition of good behaviour, the state-owned Herald newspaper said.
He is the first senior Mugabe-era official to be convicted since President Emmerson Mnangagwa took office in November after the military ousted the long-time leader.
Undenge was found guilty of awarding a public relations service contract to a company owned by a top ZANU-PF ruling party official, without going to a public tender. The firm was paid $12,000.
"Undenge has been jailed effective two-and-half years for abuse of public office after he handpicked a public relations company for the Zimbabwe Power Company without going to tender," the newspaper said.
Mnangagwa has vowed his government will not tolerate corruption.
But his critics say the 75-year-old has done little to tame graft, accusing his administration of ignoring suspected corrupt senior officials.
Several ministers from Mugabe's government were arrested for corruption and abuse of office in the months following the forced resignation of the 93-year-old veteran leader.
They included former finance minister Ignatious Chombo, ex-mining minister Walter Chidhakwa and ex-sports minister Makhosini Hlongwane, who are facing corruption and criminal abuse of office charges. Their trials are ongoing.
Zimbabwe holds elections on July 30, the first after the ouster of Mugabe.
A new poll released Friday showed Mnangagwa with only a narrow lead over opposition leader Nelson Chamisa in the landmark vote.
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