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."
The IT systems of three US hospitals have been infected with ransomware, which encrypts vital files and demands money to unlock them.