Teenager Jonty Bravery is serving a 15-year sentence for the attempted murder of the seven-year-old child.
The 27-year-old was arrested in the Selly Oak area at 4am on Monday.
The victim, a man in his fifties, is in a life-threatening condition.
Bravery was a 'looked-after child' under the care of Hammersmith and Fulham council at the time of his murder attempt.
Bravery, 18, admitted attempted murder after throwing the six-year-old boy from the 10th floor.
A 29-year-old is arrested on suspicion of attempted murder. The incident is not being treated as terror-related by police.
The six-year-old boy suffered a bleed on the brain and fractures to his spine, legs and arms.
Dom Ansah and Ben Gillham-Rice were both stabbed to death last month.
Two men have already been charged following the double murder.
Earl Bevans, 22, was charged with two counts of murder and two counts of attempted murder on Friday.