Over the past few days, voters in various districts began receiving messages praising the government's work.
Written in the local Shona language, the texts were personalized to include the name of the recipients' district - and signed "President ED Mnangagwa".
Team Pachedu, a pressure group, accused the Zimbabwe Electoral Commission (ZEC) of having passed voters' data to ZANU-PF in breach of privacy and electoral rules.
Zimbabweans head to the polls later this year in what is expected to be a tense general election, with the ruling ZANU-PF accused of cracking down on opposition voices.
Opposition parties and rights groups have complained of an escalating clampdown and raised concerns about electoral irregularities ahead of the vote.
"The messages being sent are not to ZANU-PF members, but to constituency voters including those in the opposition who never supplied their personal details to ZANU-PF," the group told AFP.
"The people receiving the messages include new registrants (virgin voters) implying that the database being used is a new one," the group said.
"(We) are looking forward to taking legal action against ZEC."
ZEC's deputy chairman Rodney Simukai Kiwa said the commission was "shocked" by learning of the SMSs but had nothing to do with it.
"We have not given anything to anyone. We do not even know what to say," he told AFP.
ZANU-PF did not respond to a request for comment.
No date has been set yet for the presidential and legislative votes, expected to be in August.
Last month, a court blocked the release of voters' rolls in electronic format, something that critics say curtails scrutiny of possible irregularities, as paper copies are expensive and hard to analyze.
And an analysis by Team Pachedu of electoral boundaries redrawn ahead of the vote showed some wards located in Antarctica.
Voters' numbers were similarly leaked and used for campaign purposes ahead of the last election in 2018 in what Team Pachedu said constituted an "intimidation tactic."