Andrew spent 11 hours in custody on his 66th birthday after allegations he shared sensitive information with Jeffrey Epstein during his time as the UK's trade envoy.
After the arrest on Thursday, UK time, detectives continued to search Andrew's former home Royal Lodge in Windsor, Berkshire, over the weekend and into Monday.
"Officers have now left the location we have been searching in Berkshire. This concludes the search activity that commenced following our arrest of a man in his sixties from Norfolk on Thursday," Assistant Chief Constable Oliver Wright said in a statement on Tuesday evening, local time.
"We understand the significant public interest in this case and our investigation remains ongoing.
"It is important that our investigators are given the time and space to progress their work. We will provide updates when it is appropriate to do so, but this is unlikely to be for some time."
Andrew has denied any wrongdoing over his links to convicted sex offender Epstein, but has not directly responded to the latest allegations.
The police statement comes after former UK envoy Peter Mandelson was arrested and later bailed on suspicion of the same offence.
Mandelson's lawyers said in a statement the 72-year-old had been arrested on Monday over a "baseless" claim he was planning to leave the country.
"Peter Mandelson was arrested yesterday despite an agreement with the police that he would attend an interview next month on a voluntary basis," his law firm Mishcon de Reya said in a statement on Tuesday.
"The arrest was prompted by a baseless suggestion that he was planning to leave the country and take up permanent residence abroad.
"There is absolutely no truth whatsoever in any such suggestion."
The firm said it had asked police for the evidence relied upon to justify Mandelson's arrest.
"Peter Mandelson's overriding priority is to co-operate with the police investigation, as he has done throughout this process, and to clear his name."
The former Labour minister has been accused of passing sensitive information to Epstein during his time as business secretary.
As part of the so-called Epstein files, emails from 2009 appear to show Mandelson passing on an assessment of potential policy measures including an "asset sales plan".
He also appeared to discuss a tax on bankers' bonuses and confirm an imminent bailout package for the euro the day before it was announced in 2010.
The emails appeared to have been sent to Epstein after he became a convicted sex offender.
Meanwhile, British Prime Minister Keir Starmer's government agreed to release documents relating to Mountbatten-Windsor's appointment as a trade envoy.
And some MPs openly questioned during a debate if it was time to end the parliamentary convention that prevents them from criticising the royal family.
Chris Bryant, a junior trade minister, said during the debate that Mountbatten-Windsor had been on "a constant self-aggrandising, self-enriching hustle" as the envoy.
Bryant called Mountbatten-Windsor "a rude, arrogant and entitled man who could not distinguish between the public interest which he said he served, and his own private interest".
MPs from opposition parties lined up to criticise Mountbatten-Windsor. At least four MPs said the convention shielding the royal family in parliament should end.
The House of Commons Speaker had given MPs approval to discuss the former prince on the basis that he is no longer a member of the royal family, having been stripped of his titles.
With Reuters
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