The International Development Secretary is to meet with the National Crime Agency over the Oxfam scandal.
Speaking about the controversy engulfing the charity, Penny Mordaunt said: "While investigations have to be completed and any potential criminal prosecuted accordingly, what is clear is that the culture that allowed this to happen needs to change and it needs to change now."
She said she would meet with the NCA on Thursday following a week of talks with charity bosses, regulators and experts.
Charities receiving UK aid have been told to show "full transparency" and outline assurances about their safeguarding processes.
"If our standards are not met, then the British taxpayer will not continue to fund them," Ms Mordaunt said.
The comments follow claims that some of Oxfam's aid workers used prostitutes in Haiti following the 2010 earthquake.
Speaking in the Swedish capital Stockholm, the minister issued a stern warning to the charity that its Government funding could be at risk over its handling of the allegations.
She said it was "not solely the actions perpetrated" by Oxfam workers but "the way the organisation responded". She said the crackdown should be a "wake-up call" to the aid sector.
The politician said the charity failed to show "moral leadership" and properly inform donors, regulators and prosecutors of the allegations.
Ms Mordaunt added: "No organisation is too big, or our work with them too complex, for me to hesitate to remove funding from them if we cannot trust them to put the beneficiaries of aid first."
She also said her department had created a new safeguarding unit to "urgently look into how we can stop sexual abusers and predators being reemployed by charities".
Officials from Oxfam are due to meet with the Charity Commission on Wednesday. A spokeswoman for the charity regulator confirmed the meeting but could not give further details.
Oxfam partners, including Marks & Spencer, Visa and Waterstones have been in touch with the charity and have said they are monitoring the situation.
A spokesperson for fellow partner Heathrow Airport said: "We are in touch with the charity and are taking this matter very seriously."
A Visa spokesperson added: "We are engaged with Oxfam to understand what steps have been taken to address staff misconduct and ensure alignment with our own standards and values."
Waterstones said it would listen to "assurances" given by the charity's bosses.
Meanwhile, actress Minnie Driver has become the first celebrity to quit as an Oxfam ambassador following the Haiti revelations.
The Government spent £13.4bn on foreign aid last year, which is 0.7% of GDP. That figure includes almost £31.7m in funding for Oxfam.
The charity also relies heavily on public donations, with £115m of its total income coming from donations, legacies and a Disasters Emergency Committee appeal. Retail sales contributed more than £90m.
Following the allegations coming to light, Oxfam issued an "unreserved apology" to the Government, donors, supporters and the people of Haiti over its handling of the claims.