Sam Busby, 18, told magistrates he was "looking for attention" when he made a string of sexually explicit comments about the five-year-old - who is now presumed murdered.
April went missing from outside her home in Machynlleth, Powys in Wales, on October 1 and despite a huge search, her body has never been found.
But call centre worker Busby put aed joke about the little girl on the social-networking site on October 6 - the day prime suspect Mark Bridger was charged with April's murder.
Worcester Magistrates Court heard the 18-year-old posted on his page: "All these April Jones jokes are getting old, unlike her."
When another user said "too soon", the teenager posted a comment about having sex with the youngster.
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The teen pleaded guilty at an earlier hearing to using a public communication network to send a message that was grossly offensive or of an indecent, obscene or menacing character.
He was sentenced to six weeks in prison suspended for 18 months and ordered to pay £185 court costs.
Chairman of the bench Gill Porter said: "You will realise by the length of time we have taken how seriously we view this.
"You caused an immense amount of distress not only to the recipients of this but to April Jones' family and friends.
"It happened at a sensitive time for everybody concerned.
"You were warned by your friends but you took no notice and you continue to make further even more offensive comments.
"They were grossly offensive."
Busby, who appeared in court wearing a grey shirt with a poppy pinned to the front, was also ordered to do 200 hours of unpaid work and made subject to a 7pm-7am curfew for eight weeks.
Kerry Lovegrove (corr), prosecuting, told the court Busby was arrested after one Facebook user reported him to police because she was so sickened by his comments.
She said: "She felt so shocked and sickened that she reported the matter to the police.
"She states that she was distressed by the comments as she herself has two young girls.
"The defendant was later interviewed where he admitted posting the joke. He admitted that he had further put the offensive comments.
"He told police he was an immature teenager and it was an attempt to get attention."
The court heard Busby told officers he thought his page could only be viewed by friends but admitted a couple of comments had come from people he did not know.
Belinda Ariss (corr), defending, said: "He is 18-years-old.
"He lives with his mother, his stepfather and two brothers.
"They are at court today but he is so ashamed of what he has done he's asked them to stay outside the court room.
"His parents and brothers don't know what he posted on Facebook but they know it must be bad.
"When he posted the initial joke it was a joke he had found elsewhere on a joke website and momentarily he thought it was funny.
"He is extremely immature. Anybody with any sense of maturity would have left it at that. Stupidly he didn't, he continued the responses.
"He's extremely sorry, he's extremely ashamed. He can't believe the extra stress he would have caused the family of April Jones."
Busby had no previous convictions and works full time as an inbound sales advisor for Serco BPO.
But the court heard he may lose his job as a result of the conviction or because the curfew will restrict his ability to work shifts.
He also plays drums for local band Dakota Ruins and describes himself as a "full-time loser" on his Twitter page.
Busby, from St John's, Worcester, refused to comment outside court.