The 47-year-old Croatian did not undertake post-match media duties following Spurs' 3-0 home defeat by Nottingham Forest on Sunday after he was informed of a family bereavement.
Assistant Bruno Saltor stepped in and declined to give further details on Tudor's "family issue".
"Everyone at Tottenham Hotspur is deeply saddened to hear of the passing of Igor Tudor's father, Mario," said a club statement on Monday.
"Our thoughts and condolences go out to Igor and his family during this incredibly difficult time."
Juventus also issued a statement expressing sympathy for their former player and manager.
"Juventus stands with Igor Tudor and his family at this difficult time," the club said on X. "Juventus joins in mourning the passing of his father."
Relegation-threatened Spurs are without a fixture for three weeks due to the international break and cup exits.
They return to action away to Sunderland on 12 April.