Mr Mphoko was due at a police station to make a statement on allegations being levelled against him but drove away when his car was approached by the officials, AFP news agency reports.
His lawyer said he feared being detained and poisoned.
Mr Mphoko was a co-vice-president under Robert Mugabe.
He served alongside current President Emmerson Mnangagwa when Mr Mugabe was ousted by the military in November 2017, but the two have fallen out.
Mr Mphoko was part of a faction that wanted Mr Mugabe’s wife, Grace, to succeed him rather than Mr Mnangagwa, the Mail and Guardian reports.
The Zimbabwe Anti-Corruption Commission (ZACC) wants to talk to him about alleged abuse of office, the newspaper adds.
Mr Mphoko’s lawyer, Zibusiso Ncube, said that his client was willing to answer questions but left when he heard “they [the police] had instructions to detain him”, AFP quotes him as saying. Mr Ncube told the Mail and Guardian that his client feared being injected “with a lethal poison”.
Earlier this month, the president fired Tourism Minister Prisca Mupfumira “for conduct inappropriate for a minister of government” after her arrest over the disappearance of millions of dollars from the country’s pension fund.
ZACC alleges the money went missing during her time as minister of labour and social welfare. Ms Mupfumira denies the allegations.