Deyka Ayan Hassan, 21, contacted officers after receiving hundreds of vitriolic responses to the message on May 22, including threats to rape her and kill her by burning down her home, Hendon Magistrates' Court heard.
But she was herself later arrested at home after admitting to police she had tweeted 'to be honest, if you wear a Help for Heroes t-shirt you deserve to be beheaded' as a 'joke' about the design of the item of clothing.
The English and politics undergraduate at Kingston University, who lives in Harrow, north west London, was ordered to do 250 hours of unpaid work by magistrates today, having admitted a charge of sending a malicious electronic message at an earlier hearing.
Chairman of the bench Nigel Orton told her she could have been jailed for what she did but that magistrates accepted she hadn’t known it was a soldier who had been killed when she posted it.
'The tragic events in Woolwich that day have created a context which made this tweet appear extreme,' he said.
'It had a huge impact and clearly caused offence and distress. We accept you didn’t intend to cause harm and you felt it was a joke.
Hassan, who was escorted to court with relatives and friends, meant her comment to be a jokey criticism of the design of the t-shirt worn by supporters of the forces charity, magistrates heard
'Your act was naive and foolish and without regard to the general public at a time of heightened sensitivity.'
The court heard that Hassan’s father works in Somalia for charities including US Aid and Prevent, combating extremism.
Magistrates accepted she hadn¿t known it was a soldier who had been killed when she posted her comment
He is also a former 'associate advisor for policing diversity' to the Metropolitan Police.
Hassan sat with her head bowed throughout this afternoon’s hearing.
The magistrates heard that she tweeted the message at around 4pm on May 22, just hours after Drummer Rigby was brutally hacked to death in south east London.
At that time, various rumours were circulating via social media about the manner of the soldier’s killing, including that he had been decapitated.
Magistrates were told that she tweeted the message to her 600 followers after seeing other people making remarks about the case and wanting to join in.
She meant it to be a jokey criticism of the design of the t-shirt worn by supporters of the forces charity, the court heard.
But after being alerted by friends Hassan found the message has sparked angry replies, including some saying she deserved to be raped or killed.
She immediately closed down her Twitter and Facebook accounts and then went to the local police station, where she was interviewed before being arrested for the original tweet.
Katie Weiss, prosecuting, said: 'She said she was making a joke about the design of the (HfH) t-shirt.
'She said it was a comment she would (typically) make about clothes and shoes she didn’t like.
Itpal Dhillon, defending, said Hassan admitted that what she wrote had caused 'gross offence' and she was disgusted with herself, having been brought up to be tolerant and respect society.
'At the time she did not know the full details relating to the horrific incident,' Ms Dhillon said.
'She certainly didn’t know that the man who was killed was a soldier and the killing may be motivated by extremist beliefs or values.
'She accepts it (the tweet) was distasteful and disgusting.'
Ms Dhillon said her client, works in a shoe shop alongside her studies. She also volunteers with charities including Crisis at Christmas and a local Somali community group.
She had not intended any 'racist undertone' to the message, Ms Dhillon said.
