Zimbabwe's main opposition party MDC Alliance says about 30 of its members have fled their homes for fear of being abducted.
The party has tweeted that some members were contemplating "moving their children to safer places".
Many fear being tortured or detained, it said.
Opposition supporters and activists called for anti-government protests towards the end of last month to decry economic mismanagement and corruption.
The government suppressed the protests by warning people to stay indoors and cracked down on solo protesters.
Those arrested have been charged with various offences that activists say have been fabricated to fall within the constitution.