"One officer has been suspended pending further investigation," Internal Affairs Minister James Baba said.
His statement did not say whether the police officer was male or female.
Ms Turinawe, who is the head of the Women's League of the FDC led by Kizza Besigye, was arrested on Friday as she tried to drive to an opposition rally just outside the capital, Kampala.
"The incident occurred during the arrest of a female who was suspected of committing a number of traffic violations and who failed to comply with the lawful instruction of a police officer," Mr Baba said.
"It is alleged that this lady suffered an assault as she resisted arrest," he added.
Ugandan television footage clearly shows that, as several officers tried to pull her out of her vehicle, another grabbed and squeezed her breast - and she is heard shouting out in pain.
The incident has sparked outrage - and on Monday a group of women stripped to their bras and marched through the centre of Kampala waving placards, including one that read "How would you feel if we squeezed your balls?"
Six protesters were arrested after they refused to put their tops back on - but they were released two hours later without charge.
Since President Yoweri Museveni's controversial re-election in 2011, opposition supporters regularly stage demonstrations - many of which have ended in violence and arrests.