Muhammad Ibn Hasan At-Tusi writes:

ولا بأس أن يتزوج الرجل متعة بكرا ليس لها أب من غير ولي ويدخل بها. فإن كانت البكر بين أبويها، وكانت دون البالغ، لم يجز له العقد عليها، إلا بإذن أبيها. وإن كانت بالغا وقد بلغت حد البلوغ، وهو تسع سنين إلى عشر، جاز له العقد عليها من غير إذن أبيها، إلا أنه لا يجوز له أن يفضي إليها والأفضل ألا يتزوجها إلا بإذن أبيها على كل حال

,,There is no problem for a man, to enter into a temporary partnership (Mut’ah) without a guardian (Wali), with an virgin female person, who does not have a father and to have sexual intercourse with her. If a virgin lives with her parents and is not an adult, then he is not allowed to have sexual intercourse with her except with the permission of her father. If she is an adult and attained the age of maturity, which is between nine and ten years, then it is permissible for him to enter into partnership with her without the permission of her father, except that it is not permissible for him, to engage in sexual intercourse with her and in any case, the most excellent thing is that he does not enter into partnership with her, except with the permission of her father.” [An-Nihayah, page 390]