Ex-Hitchin Town player Alfie Barker has been suspended from all football activity until August 1, Press Association Sport understands.
The ban, which also includes a £250 fine, comes as a result of tweets which he sent to Bournemouth midfielder Harry Arter during the Cherries' 3-3 draw with Arsenal on January 3.
The tweets from an account in the name of Barker included one which said: "at least you didn't lose your kid."
It was then followed up by another tweet to the player which said: "big hype just for a disappointment like the 9 months leading up to your childs birth."
Arter and his partner Rachel's daughter Renee was stillborn in December 2015.
Barker was sacked by Hitchin after sending the tweets. Barker apologised for what he called his "disgraceful comments" in January, and he admitted a Football Association charge at a hearing on Tuesday.
The tweets were originally reported directly to Twitter after Bournemouth and Arter became aware of the posts following the Premier League game.