Rosdeep Kular, 33, was first detained after the remains of her son were found in woodland in Kirkcaldy, Fife, late on Friday night. Last night, she was still in custody. She is expected to appear at Edinburgh Sheriff Court on Monday.
The body was removed yesterday around 3pm from a wooded area behind a bungalow in Dunvegan Avenue.
In a press conference at 11pm outside Fettes Police headquarters in Edinburgh last night, assistant chief constable Malcolm Graham said: "I would like to again recognise and thank everyone for the overwhelming levels of public support and assistance that we have seen during the course of this investigation, including family and friends of Mikaeel with whom our sympathies remain."
The investigation "continued at pace" yesterday, he said, centring on a number of locations in Edinburgh and Fife, following the discovery of a body on Friday night.
Graham said more than 200 volunteers had assisted with the search for Mikaeel in Edinburgh in adverse weather conditions and low temperatures, and police had received more than 500 calls from members of the public. Volunteers had also provided equipment and resources.
Graham added: "The investigation continues led by the major investigation teams of Police Scotland and supported by a range of local,regional and national specialist assets."
After detaining Rosdeep Kular at around 11pm on Friday night, police had just 24 hours to either release or charge her under Scots law.
Mikaeel was reported missing from his home in Ferry Gait Crescent, Edinburgh, which he shared with his mother, twin sister and three other siblings, on Thursday morning, sparking a major hunt.
Locals volunteered to search the neighbouring area and a UK-wide Child Rescue Alert was triggered for only the second time - the first being for April Jones in October 2012.
Earlier yesterday, Scotland's First Minister Alex Salmond said the discovery of a body was "the news we have all been dreading."
"The hearts of everyone across Scotland and beyond have been touched by the events of recent days. We should at this difficult time remember the work of the officers of Police Scotland who have responded to this difficult task and investigation and shown such professionalism and dedication."
The news that the body of a young child had been found was announced at a press conference shortly after 1am on Saturday morning at which Graham said: "As a result of inquiries, the body of a young child was recovered in Fife just before midnight. We strongly believe this to be the body of Mikaeel. A person has been detained in connection with the recovery of the body and members of Mikaeel's family have been informed of the recovery."
It had also emerged Mikaeel had not been at nursery since the Christmas break because of illness.
Almost 48 hours after Mikaeel went missing, police said they had "grave concerns" for his safety and that he may have been the victim of a crime.
In response to alleged offensive comments made on Twitter regarding the disappearance of the toddler, two man were arrested today.
Derbyshire Police made one arrest with assistance colleagues at Police Scotland.
A force spokesman said: "Officers arrested the 26-year-old Heanor man this morning on suspicion of committing a racially aggravated public order offence.
"Members of the public in Edinburgh had complained about the content of some Twitter messages linked to the disappearance of three-year-old Mikaeel Kular.
"The man was questioned and released on police bail while the Crown Prosecution Service considers the case."
And Police Scotland confirmed a 19-year-old man had also been arrested with the assistance of Hampshire Police, over remarks "of a racist nature" allegedly posted to the social media site Twitter.
He has since been bailed while enquiries continue.
A force spokesman said, in both cases, the remarks made online were reported to police by concerned members of the public.
He added that officers from Police Scotland then liaised with colleagues from Hampshire Constabulary and Derbyshire Constabulary to identify the individuals responsible for the posts.
Chief Supt Mark Williams, Police Scotland Edinburgh divisional commander, said: "Any reports of racist, offensive or abusive comments made online will be thoroughly investigated.
"If you commit an offence, we will investigate it and you will be prosecuted."