WASHINGTON—A translator working for the Federal Bureau of Investigation had a personal relationship with a terrorism suspect whose calls he translated as part of his duties for the bureau, according to documents from federal prosecutors made public Monday.

Abdirizak Jaji Raghe Wehelie, who was arrested over the weekend, is alleged to have covered up the fact that a person under surveillance by the U.S. government left him a voice mail on his phone—which he later translated as part of his FBI duties without noting he was the...