Rosdeep Kular, 33, was taken under guard from Cornton Vale women's prison, near Stirling, to a funeral parlour in Kirkcaldy, Fife, where the three-year-old's body was being kept.
The visit is understood to have taken place on Tuesday, the day before Mikaeel was laid to rest. Kular was not present at the funeral service at Kirkcaldy Crematorium.
A spokesman for the Scottish Prison Service said: "We do not comment on individual prisoners."
Kular has appeared in private twice at Edinburgh Sheriff Court charged with her son's murder and attempting to defeat the ends of justice. She made no plea or declaration and was remanded in custody.
Mikaeel's body was discovered in woodland in Fife on January 17, the day after he was reported missing from his home in the Drylaw area of Edinburgh.
Following his disappearance, Police Scotland issued his picture and appealed to the public for help in finding him. Hundreds of volunteers from the local community joined police and specialist teams as they searched the surrounding area.
In the early hours of January 18, police revealed that the body of a young boy had been found and that a woman had been detained.
Investigations were focused in an area of woodland behind a house in Kirkcaldy.
Kular was formally arrested and charged in connection with her son's death later that day.