It is thought the arrests relate to an incident last month in Salford when a Jewish couple were terrorised during a 4am burglary on Shavuot.
Assistant Chief Constable Terry Sweeney said: "Understandably there may be families in our communities who are anxious that they too might be targeted.
"What today is all about is taking a stand against these criminals and sending out a message that we will not allow innocent members of our community to be terrorised and have their family jewellery stolen.”
Community leaders and councillors joined police as the arrest warrants were carried out.
The four people arrested are being questioned by officers and have not yet been charged.