They believe the 23-year-old man in custody is the boyfriend of a woman injured in the fire.
And they say he may have been involved in a fight outside the building before the blaze. Later, a man was seen returning to the building with a red container, possibly filled with gasoline.
"There was an altercation prior to the fire and that may have led to the fire," said Police Chief Ron Henderson. "We're very, very sure that we have the person responsible."
Three children were found dead outside a closet in an apartment on the third floor of the three-story brick building.
Three others were unconscious, huddled together inside the closet. They died later.
"It's a tragic waste of human life," said Fire Chief Neil Svetanics.
Fire officials say the children ranged in age from seven-months to nine-years-old. They say they believed the apartment housed one family.
The woman, who apparently was the only adult inside the apartment, suffered a broken leg and head injuries after falling from her window.
She had lost her grip while desperately shouting to firefighters, witnesses said, and continued her pleas even after falling.
The scene of the deadliest blaze in St. Louis since 1988 moved many firefighters to tears, according to Svetanics.
Said a drenched and soot-covered Firefighter Tim Dangos, "This was bad ... I've been on for 14 years, and I've never seen one this bad."