The boy was reportedly thrown from the 10th floor viewing platform of the attraction in central London on Sunday afternoon and was found on a fifth floor roof, police said.
He was rushed to hospital by helicopter. His mother was heard by witnesses screaming "Where's my son, where's my son?."
Police said the injured boy remained in a critical but stable condition.
"Officers continue to work hard to establish the circumstances of yesterday's incident," police said in a statement. "The six-year-old boy's condition remains the same and officers are supporting his family."
A 17-year-old male was arrested on suspicion of attempted murder and remains in custody, police said. The teenager had remained with members of the public on the viewing platform after the boy's fall.
"There is nothing to suggest that he is known to the victim," police said.The Tate Modern, situated in a former power station next to the River Thames, was the most popular attraction in Britain in 2018 with almost 6 million visitors, according to the Association of Leading Visitor Attractions.