The unit is closing for births from Friday evening, with some expectant mothers likely to be sent to New Cross Hospital.
Mothers-to-be who were booked in at the unit are being contacted and offered alternative options for after it shuts at 5pm on Friday, health chiefs say.
The site is run by Walsall Healthcare NHS Trust, which only this week suspended its home birth service.
However the delivery suite at Walsall Manor Hospital is still open.
Carla Jones-Charles, divisional director of midwifery at Walsall Healthcare NHS Trust, said: "We would like to apologise for any inconvenience this temporary closure may cause.
"The safety of women and babies using our maternity services continues to be our number one priority.
"To do so we want to make sure we have the very best teams in the right place and are consolidating our services to ensure we continue to deliver high-quality, safe, birthing experiences.
"Any women already booked to deliver at the MLU within the next few weeks will be contacted to discuss their options.
"Antenatal and postnatal sessions will however continue as normal and mums-to-be should contact their community midwife if they have any concerns or questions."
The hospital trust's home birth service was paused in a bid to ensure midwives don't catch Covid-19 or get "pinged" by the NHS app, with health chiefs saying it needed to "ensure the safety and stability of maternity services".