The club said it was reacting to “security intelligence”, adding the restriction was in line with new checks on electronic equipment at airports.
It said that unlike at airports, it would be “impractical” at the stadium to check the devices were genuine by asking for them to be powered up.
Greater Manchester Police said it was not involved with the ban “in any way”.
A statement on the club’s site says the ban extends to large and small tablets “including iPad minis”, as well as larger electronic devices.
Smartphones are still permitted as long as their dimensions are smaller than 15cm by 10cm (5.9in by 3.9in).
“The regulations at each stadium are a matter for the relevant stadium management authorities, however, the scale of Old Trafford and profile of Manchester United mean that the risk at this venue is unique,” it adds.
A spokesman for the club told the BBC it had made the move after receiving “advice”, but would not say from whom this had come.
He added the action was unrelated to concerns about fans using tablets to record video of matches, potentially blocking the view of others, as had been reported elsewhere.
A spokesman for the Premier League said: “This is not something we are responsible for or involved in.”
The Football Association was unable to provide comment at this time.
The government announced in July that passengers flying to the US or elsewhere who passed through UK airports needed to show that devices carried in their hand luggage were charged and could be powered on. The move followed a warning that US officials had become aware of a “credible” unnamed terrorist threat.
The airport restrictions cover phones, MP3 players and cameras in addition to larger kit.