The FRP said 167 employees had been made redundant, including all players and coaching staff, leaving players in tears according to reports.
A small number of employees were retained to help with the "orderly wind down of the company", administrators said.
The club could also face relegation, along with Worcester, unless it proves a "no fault" solvency event due to the Covid-19 pandemic.
Wasps, who pulled out of its Premiership match against Exeter scheduled for Saturday, has a debt of £35 million ($70 million) stemming from its relocation to Coventry in central England from London in 2014.
The club was also hit with a winding-up order from tax authorities for £2 million ($4m) in unpaid tax.
Joint administrator Andrew Sheridan said: "This is a dark day for English rugby, and we know this will be devastating news for every Wasps player and member of staff, past players, sponsors, and their thousands of supporters throughout the world, and anyone who has ever been involved with this great club.
"Our immediate focus is on supporting those who have lost their jobs this morning."
He added that administrators "worked tirelessly" to find a solution but failed to do so.
Wasps, a two-time European champion and six-time English champion, has been an ever-present in the Premiership since the competition began 25 years ago and had some of England's top players like Lawrence Dallaglio and Simon Shaw. Its current squad contains a number of England internationals, including Jack Willis, Joe Launchbury and Jacob Umaga.
Former Wasps fly-half Andy Goode tweeted: "Exceptionally sad day for @WaspsRugby as they go into administration. A club I loved my time with on and off the field. Thoughts with every player, member of staff and fan at the minute. Hopefully the club finds new investment and can bounce back asap."
Rugby Football Union chief executive Bill Sweeney on Monday threw support behind a 10-team Premiership to help solve the English top flight's financial crisis.
"I don't know if 10 is the absolute number but that's the one being used now, but in that and the central distribution around broadcast and commercial revenues, clearly there's a financial benefit for fewer teams in that league," he said.
- with AP