Office of Grand Ayatollah Khamenei (may Allah grant him long life):
As a measure of obligatory precaution, father's permission is necessary in a marriage with a virgin girl. Without his permission, the marriage contract is not valid even in the given case as an obligatory precaution.
Office of Grand Ayatollah Makarem Shirazi (may Allah grant him long life):
In case the elders of the girl's family confirm that the suitor is the girl's equal (kufw) as well as suitable for her and the girl does not have access to her father, they can marry each other.
Office of Grand Ayatollah Sistani (may Allah grant him long life):
Yes, father's permission is required.
Office of Grand Ayatollah Saafi (may Allah grant him long life):
In the said case, her father's permission is necessary as a measure of precaution.
An answer given by Ayatollah Hadavi Teharni (may Allah grant him long life) to the above question is as follows:
In places where the father's permission for marriage of a virgin is required – that is when a girl is not mature and is not in a position to distinguish her best interest – in this case in which the father has relegated all the authority in regards to the children to their mother, mother's permission would suffice for the marriage to be valid.