She tweeted: "Since when is showing affection to someone you love illegal?"
"This is an outrage. I demand a public apology by SouthwestAir and a refund. Hate is not a family value. I will never fly this airline."
TMZ.com reported a SouthwestAir representative had replied to one of the star's tweets with an apology, and asked her to get in touch with the company privately to talk things over.
Hailey said she had taken audio and video recordings of the incident.
Southwest Airlines made headlines earlier this month when its staff kicked Green Day lead singer Billie Joe Armstrong off a domestic US flight for refusing to pull up his sagging pants.
A tweet posted on the singer's Twitter account after the confrontation said: "Just got kicked off a southwest flight because my pants sagged too low! What the f***? No joke!"
Southwest Airlines apologised to Armstrong over the incident and allowed him on the next flight to LA.
Director and actor Kevin Smith was also kicked off a Southwest Airlines flight in 2010.
The airline told the Zack And Miri Make A Porno director he could not go on a flight from Oakland to Burbank as he didn't fit properly in a single seat.
Smith objected to the decision, telling his Twitter followers: "I'm way fat, but I'm not there just yet."
He lost nearly 30 kilograms after the incident.
- Herald online