Sleep is "really important," he said in an interview on CNBC's " Squawk Box " on Tuesday. "Being present in the workplace and making better decisions has a lot to do with our business fundamentals."
"You can't be prepared if you're half-asleep," Bertolini added, saying he has the numbers to back-up his assertion that better sleep can lead to bigger profits.
Bertolini said he started a program last year to encourage Aetna employees to get more sleep and earn extra money.
"If they can prove they get 20 nights of sleep for seven hours or more in a row, we will give them $25 a night, up $500 a year," he said, explaining Aetna uses various ways to help workers keep track, including the use of Fitbit fitness trackers.
McKinsey said it conducted a recent sleep survey of 196 business leaders and found 47 percent of the respondents said their organizations expect them to be too responsive to emails and phone calls.
Some 43 percent said say they don't get enough sleep at least four nights a week, with nearly six out of 10 saying they don't sleep enough at least three nights a week.
Aetna brought in Duke University to study the effectiveness of the firm's wellness program, which includes better sleep information, yoga, and meditation. Bertolini said he's seen "69 minutes more a month of [worker] productivity on the part of us just investing in wellness and mindfulness."
"If we can make … business fundamentals better by investing in our people, then that's going to show up in our revenue," he continued. "It's going to show up in our bottom line and the Street's confidence that we can do it quarter, after quarter, after quarter; year after year."
The National Institutes of Health recommends adults, including the elderly, get seven to eight hours of sleep per night.
Arianna Huffington, co-founder and editor-in-chief of The Huffington Post, who wrote a new book about the importance of sleep, told CNBC the Aetna approach helps knock down an old business stereotype.
"It really changes the cultural delusion that most businesses have been operating under, which has been ... the more exhausted and burned out the employees are, the more productive they are," said Huffington, appearing with Bertolini on "Squawk Box."
Huffington's book, "The Sleep Revolution," was released Tuesday.
In it, she said there are number of business leaders who pride themselves on getting enough sleep, including economist Mohamed El-Erian , Hootsuite CEO Ryan Holmes, Microsoft CEO Satya Nadella , Amazon CEO Jeff Bezos , venture capitalist Marc Andreessen , and Eric Schmidt , chairman of Google parent Alphabet .