It is alleged that Jamie Milligan, 24, from Paisley, posted comments regarding the death of the three-year-old that were "grossly offensive" between January 17 and 19 while acting in a manner which was threatening or abusive and likely to cause fear and alarm to others.
Mr Milligan is also charged with posting a further comment on Facebook in the same period in which he threatened to rape a named female, placing her in a state of fear and alarm.
He made no plea or declaration when he appeared on petition at Paisley Sheriff Court, and was released on bail.
Earlier this week two men from south of the Border were arrested after allegedly racist comments apparently relating to Mikaeel's disappearance were posted on social media sites.
The two, aged 19 and 26, were released on bail following questioning.
A number of online pages have been set up offering tribute to Mikaeel with one having 77,300 supporters and another set up to organise a tribute event called Send Off For Mikaeel. As many as 1000 members of both the Fife and Edinburgh communities affected by the case are expected to launch balloons on either side of the Firth of Forth on Friday night.
The boy's mother, Rosdeep Adekoya, was charged on Monday with his murder and attempting to defeat the ends of justice.
She made no plea or declaration and was remanded in custody and committed for further examination. She is expected to appear again in court on January 28.