The institute says the bill's sponsor, Representative Frank Niceley, is withdrawing it following widespread public opposition.
Opponents included Tennessee Volunteers for Animal Protection, singer Willie Nelson, his daughter Amy Nelson and granddaughter Raelyn Nelson, long-time supporters of the Animal Welfare Institute.
"We are pleased that Representative Niceley has agreed to pull his bill from consideration," said Chris Heyde, deputy director of the institute.
"There are many more humane and responsible ways of caring for horses in need and we look forward to expanding those in Tennessee. Slaughter certainly isn't an option and we feel many legislators realised this."
Amy and Raelyn Nelson, residents of Tennessee, testified against the bill during a committee hearing earlier this month and plan on returning to Nashville to meet with legislators to discuss equine welfare issues soon.
Amy Nelson said they had got to know Nicely over the last few weeks.
"He really was listening to the facts against horse slaughter and we are grateful for that," she said.
"We're looking forward to exchanging ideas with him regarding end-of-life decisions for at-risk horses."