The systems, at Kentucky Methodist Hospital, Chino Valley Medical Center and Desert Valley Hospital, California, are now running normally again.
None of the hospitals is believed to have paid the ransom.
And the cases are now being investigated by the FBI.
The Kentucky Methodist Hospital had to shut down all of its desktop computers and activate a back-up system.
A message on its homepage said: "Methodist Hospital is currently working in an internal state of emergency due to a computer virus that has limited our use of electronic web-based services.
"We are currently working to resolve this issue, until then we will have limited access to web-based services and electronic communications."
It later said no patient data or care had been affected.
Fred Ortega, a spokesman for Prime Healthcare Services, which owns Chino Valley Medical Center and Desert Valley Hospital, said: "It did cause significant disruptions of our IT systems.
"However, most of the systems and the critical infrastructure has been brought back online."
The attack comes weeks after it was revealed Hollywood Presbyterian Medical Centre in Los Angeles had been attacked by ransomware.
In that case, it paid $17,000 to get access to files back.
Kentucky Methodist Hospital information systems director Jamie Reid named the malware involved as Locky, a new bug that encrypts files, documents and images and renames them with the extension .locky.
The most common way Locky gets itself on machines is via a spam email with an attached document that looks like nonsense and advises readers to enable macros "if the data encoding is incorrect".
Once the malware is downloaded, it sends a message to desktops with instructions about how users can pay to have files unlocked.
In November, a report from Intel's McAfee labs said the number of ransomware attacks was expected to grow in 2016.
Security expert Brian Krebs said: "It's a fair bet that as ransomware attacks and attackers mature, these schemes will slowly become more targeted.
"I also worry that these more deliberate attackers will take a bit more time to discern how much the data they've encrypted is really worth, and precisely how much the victim might be willing to pay to get it back."

Boro were the busiest Premier League club in July, making a total of eight new signings.
"We are not in a rush. We have the nucleus of the team so we just need to keep going," Karanka told BBC Tees.
"The better players we have, the more chance we have to stay in the Premier League."
Having narrowly missed promotion via the play-offs in 2015, Boro drew with promotion rivals Brighton on the final day of last season to earn promotion on goal difference and seal a return to the top flight after a seven-year absence.
The Teesside club have since been unbeaten throughout pre-season, but went a goal down after only 14 minutes of their 3-1 win over Aston Villa on Saturday - and Karanka is concerned about defensive frailties.
The 42-year old continued: "We need more [players], especially central defenders. That's the danger, where we need to improve.
"I don't want to put all the pressure on Dael Fry for example. He's brilliant, his future is more than brilliant and he's improving a lot every single day.
"But he needs to keep going forward doing the right steps and for that reason I think we need to bring [more players]."
Whilst Karanka wishes to bolster his defence, the Spaniard's priority is that any new signings fit into the team quickly.
"The main things for me is that [the new players] are settled in the team really well," he added.
"We are mixing players who two-and-a-half years ago were fighting to stay in the Championship with players who were playing in the Champions League two years ago, one year ago.
"But the spirit of the changing room is the same."
Middlesbrough will begin their Premier League campaign at home on Saturday, 13 August against Stoke City.
The IT systems of three US hospitals have been infected with ransomware, which encrypts vital files and demands money to unlock them.
[NEXT_CONCEPT]
Boss Aitor Karanka says Middlesbrough are in no hurry to make further signings as they prepare to return to the Premier League.