The school he worked at has denied accusations that he had been promoting Christianity, insisting that he highly respected Islam.
A text message circulated by mobile phone shortly after the victim, Joel Shrum, was shot dead. The message said "holy warriors" had killed "a senior missionary" in the central city of Taiz.
A statement from the International Training Development Centre in Taiz identified Shrum, who had been living in Yemen with his wife and two children since 2010.
It was impossible to confirm the claim of responsibility. Al-Qaida and other militant groups are active in Yemen, which has suffered a breakdown of central state authority during the country's yearlong uprising. Taiz security director Ali al-Saidi said Monday that the investigation is still ongoing.
The Associated Press contributed to this report.