The call came from two investment groups that hold $2bn (£1.48bn) of Apple stock between them.
A letter calling for the digital locks, signed by Jana Partners and a California teachers' pension fund, was sent to the iPhone maker this weekend.
The call for better controls was welcomed by academics studying youngsters' use of technology.
Jana Partners and the California State Teachers' Retirement System (CalSTRS) called on Apple to consider the impact excessive use of smartphones had on the mental health of young people.
In their letter, the two pointed to numerous studies which suggest excessive phone use can disrupt lessons, harm students' ability to concentrate on school work and deprive them of sleep.
The document also mentioned the impact that "heavy use" of social media can have on self-esteem and its possible influence on childhood depression.
The two are worried that if Apple does not address growing concerns about smartphone use, its stock market value and general reputation could be damaged.
According to a Reuters report, half of US teenagers believe they are addicted to their mobile phones and feel the need to respond immediately to messages.
The investment groups acknowledged that a variety of factors were at work in determining a young person's outlook and mental health. But, they added, it "would defy common sense" to argue that high levels of phone use were not having some impact.
The makers of such "powerful products" also needed to help parents ensure phones are being used optimally. They called on Apple to improve its current parental control systems which, they said, were a "binary, all or nothing approach".
The two groups said they would welcome the chance to talk about the issues they raised with Apple's board of directors.
Sonia Livingstone, professor of social psychology at the London School of Economics, said it was good to hear the call from the investors.
She added there needed to be one voice between device manufacturers, social media companies and internet service providers (ISPs) on the issue of smartphone use.
"For a long time the concern has been to not do anything that would impact a friction-free experience," Prof Livingstone told the BBC.
"Everyone would like to have a well balanced life, but the way that devices are designed currently causes a lot of conflict with parents."
She called on Apple and other device manufacturers to have all notifications on smartphones switched off by default and for the creation of occasional reminders that urged youngsters to take a break from their phone after long periods of use.
Prof Livingstone, who also runs a parenting blog, did question the use of the term "addiction" for those who spend a long time using a smartphone, however.
"Everyone will agree that there is excessive use and even obsession with smartphones, but I don't believe it's addiction," she said.
Apple has not yet responded to requests for comment.