Administrators were appointed after the private companies of News Corp co-chairman Murdoch and regional TV boss Bruce Gordon declined to extend support for a debt facility past 2017, the network said in a statement.
Sydney-based Ten said the unusual move would help it re-negotiate costly content licensing fees with U.S. production studios like CBS Corp, and added that its directors "regret very much that these circumstances have come to pass".
Murdoch and Gordon had "agreed to work together exclusively to facilitate the potential formulation, negotiation and implementation of a restructure proposal", they said in a regulatory filing to the Australian Securities Exchange.
Murdoch and Gordon, who jointly control about 22 percent of Ten's shares, had not yet agreed on terms of that proposal, it added.
Administrators Mark Korda, Jenny Nettleton and Jarrod Villani, from KordaMentha, said in a statement they were "confident that the network is an attractive asset which will find a buyer or will be capitalised".
They did not name a potential buyer.
Pay-TV company Foxtel, which owns 14 percent of Ten, has long been touted as its most likely buyer, although that would be stopped by current media ownership restrictions. Foxtel declined comment.
Broadcasters and Ten in particular have suffered large losses as advertisers follow viewers onto streaming services like Netflix and Amazon.com Inc's Amazon Prime.
Ten said it has already agreed, on an informal basis, to new licensing deals with CBS and Twenty-First Century Fox Inc which would halve its future liabilities while still allowing it access to those studios' productions over the medium term.
As well as its reality television-heavy programming, the perpetual ratings laggard uses content deals with those U.S. studios to air shows such as NCIS and CSI: Crime Scene Investigation.
Ten's predicament adds to pressure on the government to deregulate media ownership and make it easier for traditional media companies to buy each other. Bills to that effect are to be tabled in parliament on Thursday, and face opposition over concerns about diversity in an already concentrated market.
A takeover by Murdoch or Gordon may face regulatory hurdles under the country's current media ownership laws.
"The Ten Network should be a wake-up call for opponents of media reform," Federal Communications Minister Mitch Fifield told reporters.
Ten said part of Fifield's package, a reduction in television licence fees, would cut overheads.
The Australian Securities Exchange suspended Ten shares indefinitely.
The stock last traded on Friday at 16 cents, having closed at A$2.56 two years earlier.
(Reporting by Byron Kaye and Jamie Freed in Sydney and Ambar Warrick in Bengaluru; Editing by Stephen Coates)
By Byron Kaye and Jamie Freed