It is not obligatory upon the woman to perform ghusl after artificial insemination and wudu’ is sufficient in this case. If the woman performs ghusl, then there nothing wrong at all and her act is a recommended one.

Dr. Muzammil H. Siddiqi, former president of the Islamic Society of North America, states:
“It is mustahabb (recommended) but it is not fard (obligatory) for a woman to perform ghusl after artificial insemination; wudu’ is sufficient. Ghusl is required for the junub person. Allah says in the Qur’an, “O you who believe, do not approach prayer when you are polluted (junub) till you have bathed.” (An-Nisaa’:43). The junub is a person who had sexual intercourse or a wet dream or who discharged semen due to lustful desire. Emission of semen without lust on account of a fall or shock or after urination, does not make ghusl necessary.”