Activists from climate group Ultima Generazione (Last Generation) burst onto the Pietrangeli court, where American Madison Keys was leading Sorana Cirstea 6-2, 3-1 in the women's last 16.
Wearing orange vests, they threw a liquid onto the court and confetti before being removed by security staff.
Two people also burst onto an adjacent court 12, where a men's doubles match was underway and also threw a liquid and confetti.
The stands were evacuated as organisers awaited the arrival of police.