The hearing had been due to end Friday, but officials at London's Royal Courts of Justice said the case before Justice Hugh Bennett would continue Monday.
Mills and McCartney separated in 2006 after four years of marriage and have since traded blows in the media while trying, and failing, to agree on divorce terms.
The hearing was called to decide on Mills' share of the former Beatle's fortune, estimated at as much as $1.6 billion. Media reports suggest that McCartney has offered his estranged wife around $50 million and that she is seeking at least double that amount.
The couple has squared off every day this week in Court 34 of the grand, gothic courthouse, but few details have emerged. Unlike most British court cases, divorce proceedings are heard in private, and the courtroom is completely closed to journalists and the public.
Mills, 40, and McCartney, 65, have made no comment to the reporters and photographers who have gathered outside court each day.
However, Sir Paul has been spotted going into the court in apparent high spirits, observes CBS News correspondent Elizabeth Palmer.
The secrecy surrounding the hearing is so complete that even the crates of documents going into court have been covered with blankets, Palmer says. But reporters did spot one of Mills' boxes, marked ''Fan Mail."
McCartney has hired lawyer Fiona Shackleton, who represented Prince Charles in his 1996 divorce from Princess Diana. Mills, who fired her legal team late last year, is representing herself.
And the strain, says Palmer, may be showing: it was reported Thursday that Mills spent 20 minutes sitting alone, looking tense in her car outside the court.
After the hearing ends, Bennett is expected to take several weeks to consider his settlement. The terms will not become public unless it is challenged in the Court of Appeal, or either of the parties chooses to reveal details.
Mills is a former model whose left leg was amputated below the knee after a motorcycle accident in 1993. She became active in campaigning against land mines and in favor of animal welfare.
The couple married in June 2002 four years after the death of McCartney's first wife, Linda and their daughter Beatrice was born in October the following year. They announced their separation in 2006, and McCartney filed for divorce alleging "unreasonable behavior" by his wife.
It's believed, Palmer reports, that Mills has been arguing that she's owed compensation because her own, thriving career as an inspirational speaker and campaigner for amputees has been ruined by her acrimonious split from the ex-Beatle. It's also reported that she is asking for money to pay for 24 hour security for both herself and her daughter.
The British tabloids are saying Friday that McCartney sent Mills a bouquet on the eve of the hearing with a note saying, "Please remember -- you and I are both human and we have one very special person in common."
"I think the big issue in this case, frankly, is not Beatrice," family lawyer Alan Kaufman told CBS News. "She will be looked after, and things will be OK for her. The massive issue is how much of paul's wealth is heather going to get?
"They both really are big, big public personas," Kaufman continued. "There's been the most massive publicity ever, frankly. This is the highest-profile divorce case ever in the world."