According to British newspaper The Sun, the mistake happened when Charlie, 46, tried to send his number via private message to pop star Justin Bieber, asking the singer to give him a call.
Instead, Sheen, who was having dinner at Las Vegas restaurant Guy Savoy, tweeted the number on his public profile, meaning that all his followers could see it.
The former Two And A Half Men star's phone then started going crazy.
Onlookers told the newspaper: 'Charlie's phone immediately went into meltdown. It was ringing wildly and he got 1,800 text messages in minutes.
'Charlie saw the funny side and answered the phone a few times, saying things like 'Ray's Pizza' and 'winning'.'
The onlookers added: 'But his phone just continued ringing and buzzing and eventually just completely melted down. Charlie was like, 'I guess I need a new phone'.'
A spokesperson for Charlie stated: 'I haven't been able to get through to him on the phone since Wednesday. He just got a new number.'