The detained are between 18 and 61 years old and were deprived of their freedom in the Manchester suburbs Prestwich and Farnworth. It is about three women and three men.
"All those deprived of their freedom have been arrested suspected of having committed, prepared and instigated terrorist acts", the police write on their website.
Two men, 53 and 66 years old, were killed in connection with the attack. One of them was shot dead by mistake by the police. Three more people were seriously injured.
The perpetrator was also shot dead by the police after he first drove into people outside the synagogue and then went on the attack with a knife. The man had what turned out to be a fake bomb belt on him
The suspected terrorist was a 35-year-old British citizen of Syrian origin.