Militants belonging to a group called Sri Ram Sena, who claim to be custodians of Indian culture, said Valentine's Day is un-Indian.
The threat comes days after the group's activists stormed a bar in the south western city of Mangalore, dragging out and beating women they accused of acting obscenely and "going astray".
The attack led to fears an extremist "Hindu Taliban" was on the rise in India.
Gangadhar Kulkarni, an activist in the group, which is a radical wing of the Hindu nationalist movement, said: "If people celebrate the day despite our warning, then we will definitely attack them."
"Valentine's Day is definitely not Indian culture. We will not allow celebration of that day in any form," added Pramod Mutalik, the group's founder.