I presume she must have had a mother at some point - or how could she be alive? But we never hear about her mother in the play - she's never mentioned once. We do, however, obviously know about Sebastian, her brother, and the two fo them, in the play's final scene, talk about their father in very affectionate terms:
What countryman? what name? what parentage?
Of Messaline: Sebastian was my father;
Such a Sebastian was my brother too:
So went he suited to his watery tomb:
If spirits can assume both form and suit
You come to fright us.
A spirit I am indeed;
But am in that dimension grossly clad
Which from the womb I did participate.
Were you a woman, as the rest goes even,
I should my tears let fall upon your cheek,
And say ‘Thrice welcome, drowned Viola!’
My father had a mole upon his brow.
And so had mine.
And died that day when Viola from her birth
Had numbered thirteen years.
So yes, Viola and Sebasitan have a father also called Sebastian. But Shakespeare makes no mention of their mother. She's one of a line of mother who goes unmentioned: Queen Lear, Mrs. Leonato in Much Ado, Mrs Duke Frederick in As You Like It... and so on.
Hope it helps!