The Crown Office has warned that any criminal conduct on websites such as Twitter and Facebook will result in prosecution.
The warning follows the arrest of two men over posts made on social media sites spotted by members of the public in Edinburgh who alerted police.
The arrest of Mikaeel's mother led to an outpouring of fury on some social media sites, with some people using strong language to make their feelings known.
However, the Crown Office warned that it will take a hard line with any people who broke the law on social media networks.
Individuals could potentially breach contempt of court or defamation laws. Even re-tweeting somebody else's abusive post would put someone at risk of breaking the law.
A Crown Office spokeswoman said: "We will continue to work with Police Scotland to investigate any criminality arising from conduct on social media, and we will prosecute wherever there is sufficient evidence and it is in the public interest to do so."
The two men arrested, aged 19 and 26 and both based in England, made comments on Twitter, police said. Both were questioned and freed on bail yesterday.
Officers from Police Scotland worked with Hampshire Constabulary and Derbyshire Constabulary to identify the two.