Reports say police locked the gates and placed barbed wire at the entrance.
Rafah is the only regular exit from Gaza for 1.6m Palestinians living there. Other crossings into the occupied territories are allowed only in exceptional cases.
The three policemen and four soldiers were captured while travelling in the peninsula, east of El Arish.
Four of the men worked at the Rafah crossing, reports said.
An Egyptian security official said the Rafah crossing will remain closed until the group is released, the Associated Press news agency reported.
The Palestinian Maan news agency said Gaza's Interior Ministry declared a state of alert along its border with Egypt and large numbers of Egyptian soldiers have been in the area.