Can a brain tumor be caused by brain infection?

No, not likely: Generally, brain tumors do not arise from brain infection (eg., meningitis, encephalitis, absess); however, a bacterial superinfection may rarely develop in a primary brain tumor.

Abscess: A brain abscess can develop from brain infection and be a tumor or growth that causes pressure on the surrounding brain. This can even mimic a more aggressive growth or tumor that arises from the brain cells themselves such as a cystic glioma. Generally once the infection is treated and the abscess drained if needed then there should be no recurrence of this kind of growth reinfection occurs.