Magistrates in Swansea, south Wales, sent 21-year-old biology undergraduate Liam Stacey to prison after he admitted the charge at a previous hearing last week. He broke down in tears as he was taken away in handcuffs on Tuesday.
Sentencing the student, district judge John Charles said there was "no alternative" to an immediate prison sentence, as when Muamba collapsed "it was not the football world who was praying for him... everybody was praying for his life".
Stacey's remarks on Twitter as the footballer battled for his life were "vile and abhorrent", the judge added.
The student was reported to police and arrested after posting a number of tweets on the micro-blogging site mocking the player, who collapsed with a cardiac arrest during Bolton's FA Cup quarter-final tie with Tottenham Hotspur on March 17.
Stacey was taken to task by other users after he used offensive language to say that the player had died, prompting him to respond with a tirade of personal abuse.
Swansea University said last week that they had suspended Stacey pending a formal disciplinary hearing.
Muamba, whom doctors said was effectively dead for 78 minutes as they administered artificial resuscitation, has since made a "miraculous" recovery but is still in a serious but stable condition in intensive care at a London hospital.
The 23-year-old midfielder was on Monday said to be making "encouraging" progress and had even managed to sit out of bed and watch television, doctors at the London Chest Hospital said in a statement.
His collapse led to the FA Cup tie being abandoned. The match is due to be replayed at Spurs' White Hart Lane ground on Tuesday night. A number of Bolton players were seen visiting their colleague in hospital ahead of the game.
In a separate case last Wednesday, magistrates in Newcastle, northeast England, ordered another student to complete a two-year community order with 240 hours unpaid work for sending a string of abusive tweets to former footballer Stan Collymore.
Newcastle University student Joshua Cryer, 21, admitted sending the messages to the former Liverpool, Aston Villa and Nottingham Forest player, who now works as a radio and television pundit.
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