The action left hundreds of Gaza residents stuck at the border, the Palestinian Ma'an news agency reported.
Police refused to open the crossing even after Egyptian Interior Minister Mohammad Ibrahim sent an assistant to Rafah to intercede. Police said they would only open the crossing when their colleagues are released.
The seven police officers and soldiers, including four who worked at the Rafah crossing, were abducted Thursday during an ambush in Sinai. Egypt stepped up security Friday, closing tunnels to Gaza, in an effort to keep the kidnapped men from being moved to Gaza.
An Egyptian official said 800 Palestinians were waiting to cross and the number was expected to grow to at least 1,000 by the end of Saturday. They included students returning from study abroad and people who had left Gaza for medical treatment.
Police also kept the airport and seaport closed in el-Arish, the closest town to Rafah on the Egyptian side of the border. Most of the stranded Palestinians were in hotels in el-Arish.