Sandwell and West Birmingham Hospital Trust said it was introducing the restrictions on all its wards and departments.
The reason is to reduce the traffic within the hospitals and also reduce the pace and risk of corona virus being spread within the hospitals.
Royal Wolverhampton NHS Trust said it was suspending visiting and introducing special measures in maternity.
Visitors for children or those receiving end-of life care will still be permitted, as will birthing partners, the trust said.
Telephone and video calls will be made available to those not allowed to visit, it said.
In addition, a “significant number” of outpatient appointments will either be rearranged or take place over the phone from Monday, the trust said.
In a statement the trust said: “We are sorry for this inconvenience as we aim to limit the spread of coronavirus”.
