The union, which represents 30,000 people in the sector, expressed its fears after housing charity Stonham and children's charity NCH lost contracts to private companies.
Stonham lost a Supporting People contract from Cornwall County Council to Clear Springs, a company that provides accommodation to asylum seekers for the Home Office.
"Stonham went into the bid at the lowest it could possibly afford," said Dave Jones, Amicus national executive committee member for the non-profit sector. "But Clear Springs was able to undercut all the not-for-profit organisations by submitting a lower price.
"Contracts should be based on best value. In this case, the cheapest provider got the contract. Our concern is that private sector organisations coming into this market are driving the standard of service down."
Andrew Painton, executive director at Stonham, which delivers services to 11,000 people each year, agreed the commissioning climate was getting tougher for charities.
"The sector has done well to position itself favourably with the Government in the public service debate," he said. "But local authorities are the ones making commercial decisions, and they are interested in price as well as quality."
A spokeswoman for Clear Springs said: "Our aim was to submit a bid that provides excellent value and an efficient service."
Amicus also attributed NCH's loss of three contracts to the private sector to its inability to compete on price. The children's charity said price was not the only factor, but would give no details.
Rachael Maskell, national officer for the not-for-profit sector at Amicus, said: "I think this trend is increasing. We are at the start of marketisation, and there's nothing in competition regulations that protects the third sector.
"But organisations aren't happy to talk about this because of the fear of losing further contracts."
A spokesman for the Confederation of British Industry, which supports contestability in public services, said that a low price for a contract did not necessarily mean that service quality would fall.
"We agree all contracts must be on the basis of best value," he said.
"If someone has been undercut by giving poor terms and conditions to staff or reducing service quality, that's unacceptable.
"However, if a company has managed to put in a lower bid by changing the way the service is delivered so it means a lower cost to the taxpayer while also maintaining or even improving service quality, everyone should welcome that."