No criminal charges have been filed, according to an unnamed official quoted by the AP news agency.
The attack on the Medecins Sans Frontieres hospital took place last October during a campaign to retake the city of Kunduz from Taliban forces.
A US military inquiry has already found that the attack was "human error".
The Pentagon is expected to release a full report on the investigation on Friday.
The service members, including some special operations personnel and one general officer, received administrative punishments, AP said.
They include letters of reprimand, which could have a career-ending effect on those involved.
An AC-130 gunship aircraft mistook the clinic for a nearby government building that had been seized by Taliban fighters.
US officials initially claimed that American forces had struck the hospital because they had come under fire from the area. The military then admitted the strike was a mistake and launched an investigation.
Medecins Sans Frontieres called the incident a war crime. In a report, the group said its staff contacted US-led forces several times during the attack, saying they were being bombed.
The charity also said the co-ordinates of the hospital were well-known and had been communicated again to all sides three days before the bombing.
It repeatedly asked for an independent international investigation into the bombardment.
Army Gen John Campbell, the top US commander in Afghanistan at the time, called the incident a "tragic but avoidable accident caused primarily by human error".
US President Barack Obama apologised for the air strike, which was one of the deadliest attacks on civilians in the 15-year Afghan conflict.
Sixteen US military personnel have been punished with disciplinary measures over the bombing of an Afghan hospital that left 42 dead, officials say.