A struggle ensued, during which the firearm was discharged. Both officers received minor injuries but were not harmed by the shot.
A firearm has been found and an area sealed off while investigations continue.
One man in his 20s has since been arrested in connection with the incident and police are continuing to search for the second man.
The incident follows the death at the weekend of Constable Richard Gray, a 43-year-old armed response officer who died after being shot during a domestic incident in Shrewsbury's Castlefields area.
Anyone with information about the incident in Birmingham has been asked to contact Rose Road police station in Birmingham or Crimestoppers.
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