A senior investigating officer made the appeal on the day Rosdeep Adekoya, 33, was brought to the dock at Edinburgh Sheriff Court.
She is accused of her son's murder and attempting to defeat the ends of justice as a huge search went on for the youngster in the capital last week.
Chief Super-intendent Mark Williams, Police Scotland's Edin-burgh divisional commander, wrote to Flora Stevenson primary school and nursery asking for "relevant information" from anyone who might have spoken to the family or have any other intelligence to feed into the wider investigation.
Mikaeel's body was found in Kirkcaldy, Fife, on Friday evening.
The requests from Chief Supt Williams, which were distributed by the school, said: "I am conscious that this is an emotional and difficult time for the community and for staff, parents and children from both the nursery and school.
"I am keen to limit the impact that the inquiry will have on the school but hope you will understand that it is imperative that I carry out a thorough and professional investigation in order to fully understand the circumstances surrounding Mikaeel's death."
He concluded: "I appreciate your support and assistance at this difficult time."
Headteacher Irene Brennan added in a separate letter to parents: "If you believe you can assist them, get in touch with them directly." She said staff had dealt "sensitively" with questions from children and a "normal" school day had taken place.
"Myself and my staff continue to be grateful for the unfailing support of parents and carers," she concluded.
Mrs Adekoya was brought to the court amid tight security cordon for a private hearing, before Sheriff Frank Crowe, that lasted a few minutes. She made no plea or declaration, was remanded in custody and committed for further examination. She is expected to re-appear in court on January 28.
Meanwhile, almost 77,000 people showed support for a tribute page to Mikaeel on the internet, days after hundreds of people turned out to help in the search for him.
Earlier, two men were arrested after allegedly racist comments apparently relating to Mikaeel's disappearance were posted online.
Mikaeel was reported missing from his home in the Drylaw area on Thursday morning and a Police Scotland operation was mobilised, with officers issuing his picture and appealing 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 on Thursday and Friday.
Coastguard teams and two helicopters also scoured the shore a mile from his home.
Floral tributes, soft toys and candles were placed at a small park and 500 attended a weekend memorial service at Muirhouse St Andrew's Church less than a mile from the home Mikaeel shared with his twin sister and three other siblings..