The "low three-figure" sum of money was taken from three purses which had been left unattended at the Aberdeen Sea Cadets base at Pocra Quay.
Insp Carron McKellar said: "This is a disgraceful incident which has left the victims shocked and upset."
Anyone with information on the theft is urged to contact Police Scotland.
Insp McKellar added: "It is understood that the suspect entered the building while visitors were in another part of the building and took the money. Nothing else has been taken."

Correspondents said the atmosphere at schools was subdued and many pupils had not returned.
They said parents had been taken by surprise by the government's decision to reopen schools with only four days' notice and many were not prepared.
More than 8,400 people have died in West Africa in the world's worst outbreak of the Ebola virus.
The reopening of schools in Guinea comes four days after the UN said the number of confirmed Ebola cases in the country had fallen to its lowest weekly total since August.
At one school in the Guinean capital, Conakry, only about 220 of the approximately 2,000 pupils were reported to have returned.
Of the 36 teachers, more than half were back at work.
Many schools have introduced health precautions, including hand-washing and temperature checks.
Ebola has had a severe impact not only on public health but also on the Guinean economy.
Unemployment and underemployment have risen, leaving many parents with difficulties meeting school-related expenses at the beginning of a new academic year.
Schools remain closed in Sierra Leone and Liberia, the two other countries hit hard by the Ebola outbreak.
Earlier this month, the outgoing head of the UN team fighting Ebola, Anthony Banbury, said he believed cases of the virus would be brought down to zero by the end of 2015.

The 34-year-old's ban now expires on 1 June 2018, instead of 25 October 2018.
He was banned in April after being charged with breaking FA rules for placing 1,260 bets on matches between 26 March 2006 and 13 May 2016.
Barton, who says he is addicted to gambling, appealed against the length of the ban which he called "excessive".
The FA's Appeal Board said the initial ban was "excessive in the circumstances" as evidence from Barton's consultant psychiatrist about his addiction should not have been rejected.
The report says the new ban "reflects the overall seriousness of the breaches and also the mitigation including the full extent of Mr Barton's addiction".
Barton, whose fine of £30,000 remained unchanged, was released from Burnley in May.
Players in England's top eight tiers are banned from betting on football.
Former Manchester City and Newcastle midfielder Barton rejoined Burnley in January, having left Scottish Premiership side Rangers in November.
In November 2016, he was given a one-match ban for breaking Scottish Football Association rules on gambling.
Barton admitted the Scottish FA charge of placing 44 bets between 1 July and 15 September 2016, while he was a player at Ibrox.
The theft of money from purses at a Remembrance Sunday event at Aberdeen harbour has been branded "disgraceful" by police.
[NEXT_CONCEPT]
Schools have been reopening in Guinea after a five-month closure because of the deadly Ebola outbreak.
[NEXT_CONCEPT]
Former Burnley midfielder Joey Barton's suspension from football for breaching betting rules has been reduced by almost five months after an appeal.