State police Trooper Charles Swiney said two children survived the crash with the tractor-trailer on northbound Interstate 65.
A pastor for the family in the van said they were Mennonites on their way to a wedding in Iowa. Authorities say the truck driver, who was from Alabama, was also killed.
Officials say the tractor-trailer crossed the median and struck the van head-on around 5:30 a.m. CDT near Munfordville, about 75 miles south of Louisville.
The National Transportation Safety Board said it was dispatching a team to investigate the crash.
Pastor Leroy Kauffman with the Marrowbone Christian Brotherhood in Burkesville, about 55 miles southeast of the crash site, says the two surviving children were taken to a nearby hospital.
Joe Middleton, a supervisor at Caverna Memorial Hospital in Horse Cave, said two survivors from the accident were taken there and released around 10 a.m.
He couldn't confirm their identities or injuries due to privacy laws, but said it was his understanding they were the only two survivors of the crash.
Kauffman said there were three young children on board ages 1, 3 and 5. He said the father was an assistant pastor at the church and there was also a couple on board the van who were engaged to be married, although they were traveling to someone else's wedding.
"They had a July wedding planned but they won't need that now," Kauffman said. "They'll have a wedding in heaven I guess."
He said the family's house burned down in December and they had just moved into a new home built by church members.
"We're experiencing a lot of heartache and a lot of sadness, but with that a hope," Kauffman said. "We know where these people are going, they were all saved Christians and walking with the Lord."
The crash is one of the most deadly traffic accidents in recent Kentucky history. On May 14, 1988, 27 people were killed in a fiery bus crash caused by a drunken driver going the wrong way on Interstate 71 in Carroll County. That bus was owned by the First Assembly of God church in Radcliff and was filled with youths returning from an amusement park.