Karen Rouse, 42, was detained by police and charged with a breach of the peace. It is alleged that she made an offensive comment on a social media website regarding Mikaeel.
She made a private appearance at Hamilton Sheriff Court where she made no plea or declaration and was released on bail.
Rouse, from Hamilton, is expected to appear again at a later date.
The toddler was reported missing from his home in Ferry Gait Crescent, Edinburgh on January 16. His body was found 25 miles away in Kirkcaldy on January 18.
Mikaeel's mother Rosdeep Kular, 33, has since appeared in court charged with his murder and attempting to defeat the ends of justice. She made no plea or declaration and was remanded in custody.