The ruling does not prevent Begum, now 21, from continuing her legal case against the British government's decision to revoke her citizenship in 2019.
After traveling to Syria, she lived in Raqqa, the capital of the self-declared caliphate, where she remained for four years until she was discovered in a detention camp.
The human rights group Liberty said the court's ruling sets "an extremely risky precedent". Its impact is likely to be felt by others who left Western nations to join the Islamic State.
Then-Home Secretary Sajid Javid stripped Begum of her citizenship in February 2019, saying that because both of Begum's parents are citizens of Bangladesh, she too was entitled to citizenship in the South Asian country.
Begum is among roughly 10,000 foreign women and children with perceived links to the Islamic State who are living in "subhuman" conditions in camps across northeastern Syria.
She said there was "no way", adding "our job is to keep our country safe".
Rights groups said that visits to camps by British authorities showed it was possible to bring detainees back home.
The Supreme Court will also rule today on whether, if refused leave to re-enter the UK, Shamima Begum's appeal against the removal of her British citizenship should be allowed.
Begum spoke to Sky News days after her third baby was born in February 2019, telling correspondent John Sparks "a lot of people should have sympathy" for her as there was no evidence she had done anything unsafe.
Although many people sympathized with the young woman, who was 19 at the time, others were dismayed by a number of comments she had made to British media outlets in interviews from the Syrian camp and her stated lack of regret about joining the Islamic State in the first place.
The case could have huge significance for the government, which has revoked the citizenship of about 150 British nationals on grounds of national security.
Her newborn baby died soon after she gave birth, while two of her other children also died under IS rule. Begum bore three children after fleeing to the Islamic State, all of whom died young.
But the country's top court overturned that decision, meaning that although she can still pursue her appeal against the decision to take away her citizenship, she cannot do that in Britain.
The court said in a unanimous ruling that her rights were not breached when she was refused permission to return.
Reed added that the Court of Appeal did not give the Home Secretary's assessment of the requirements to enter the United Kingdom "the respect it deserved", adding that the court made their "own assessment of the requirements" despite an "absence of relevant evidence".
In July previous year, the Court of Appeal ruled that "the only way in which she can have a fair and effective appeal is to be permitted to come into the United Kingdom to pursue her appeal". This is "not a ideal solution as it is not known how long it may be before that is possible", he said.