Sir David Thompson said rising Covid cases meant it had become increasingly difficult to "ensure that resilience is not compromised" due to large numbers of officers and staff being off through self-isolation.
He called on the Government to "explore all opportunities" to quickly introduce a test and release scheme for policing, making it easier for forces to meet demand.
The latest official figures show West Midlands Police was the only force in the country to see a rise in crime in the year to March, while it is dealing with more than 6,000 calls a day to 101 and 999 services.
Sir David said in a statement: "This week the country entered a new phase in the pandemic as many of the remaining Covid restrictions were removed.
"The Government has set out the terms of how we do this in a way that follows the science and is pragmatic and enables it to meet its fundamental obligation of suppressing the virus and keeping people safe.
“Since the start of the pandemic, policing has been at the forefront of the response to managing the virus and is acutely aware of the risks and issues related to it.
"However, as infection rates remain high it is becoming increasingly challenging within West Midlands Police, like many other forces, to ensure that resilience is not compromised with high self-isolation through track and trace or other notifications.
“Against this backdrop, it is critical that we explore all opportunities with Government to introduce a test and release scheme swiftly for policing which makes it easier for us to free up resources and meet demand at what is already an exceptionally busy time of the year with very high volumes of calls.
"Any exemptions granted would be applied carefully in a responsible way so as not to compromise the safety of colleagues or the public.
“I understand how challenging this is, but we need to do everything we can to ensure we can deliver sustainable policing services and keep the public safe."