Contact tracing is one of the main ways to stop the virus spreading: finding everyone who has been near an infected person and placing them in isolation.
Frontline workers are going unpaid, are poorly trained and are short of supplies, the medical charity said, and some ambulances have run out of fuel.
More than 5,400 people have died and 11,000 have been infected since the outbreak was declared in May, the BBC reported, making it the second-most deadly Ebola outbreak on record.
In its report, MSF said:"Despite the vast amounts of money provided for the response, many frontline responders are left trying to contain the outbreak with empty hands and empty pockets.".
The epicentre is in eastern Congo, a region wracked by conflict for decades, with some affected areas under rebel control.
In both provinces hit by the outbreak, MSF said it observed teams that were"inadequately resourced to respond effectively.".
Health facilities lacked essential items including water, chlorine and triage systems, the charity said.
Medical staff are going unpaid, lack proper training and are struggling with shortages of essential supplies, MSF warned.
MSF said the gap between funds provided for the response and conditions on the ground was leaving many responders unable to contain the outbreak where it is spreading.