System outages at CVS Health pharmacies are due to an "internal network infrastructure issue," non-executive Chairman David Dorman told CNBC on Wednesday.

The cause is not known yet, he said.

Dorman said top management notified him about the network issue after customers around the nation complained about not being able to refill their medications.

Shares of CVS opened lower on Wednesday after falling 1.4 percent on Tuesday.

Customers have taken to social media to speak out about their complaints.

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In a statement released on Twitter to customers, CVS said, "some of our pharmacies are experiencing system connectivity interruptions that we are actively working to resolve."

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CNBC reached out again to CVS on Wednesday morning for any new details.

A CVS spokesman stated, "In investigating yesterday's outage we found an issue with a component of our network. As part of our network recovery process, there was a procedural error that resulted in a longer than expected recovery."

—Reporting by CNBC's Becky Quick.