Shadow foreign secretary Emily Thornberry also warned that UK personnel risk being "witnesses to war crimes" if the report was correct in saying they have been fighting on the same side as militia which use child soldiers.
Mr Field said he would not comment on UK special forces, in line with Government policy.
However, he suggested the allegations linked to child soldiers would be "investigated as a matter of urgency".
Mr Field was standing in to answer the question after Alistair Burt resigned as Middle East minister on Monday over Brexit.
Thousands of people have been killed in Yemen's four-year civil war.
Iran-backed Houthi rebels have been fighting against a coalition led by Saudi Arabia in support of the internationally recognised government of Yemen.