The South Belfast MLA was speaking after the Wellington Park building was daubed with red paint.
Ms Bradshaw said the incident should be treated as a hate crime.
“This attack is disgusting – Belfast Islamic Centre contributes much to the cultural life of South Belfast and beyond, and I utterly condemn those who carried this out, who are unrepresentative of the vast majority of people in the wider area.
“Those who take part in such hate-filled actions seek to drive a wedge between communities and heighten tensions, both racial and religious. They have no place in our society, and we must unite and stand steadfast in order to defeat them.
“If anyone has information about this attack, I would urge them to contact police immediately.”