The 16-year-old was in woodland, between Howitts Lane and Howitts Gardens, in St Neots, at about 17:30 BST, when he came off his bike.
He suffered serious injuries to his neck and wind pipe, Cambridgeshire Police said.
He was rushed to Addenbrooke's Hospital where he remains in a serious but stable condition.
Det Con Diane Tomlinson said: "The young man is in a serious condition in hospital and I would like to speak with anyone who may know why the rope was tied to those trees, or who may have put it there.
"Anyone who uses the area, such as dog walkers, who may have information, no matter how insignificant it may seem, should call police."

The national service was held in Cardiff, with a march from King Edward VII Avenue to the Welsh National War Memorial in Alexandra Gardens.
Among the other towns and cities holding services were Aberystwyth, Bangor, Swansea, Wrexham and Newport.
Volunteer Brian Thomson, 64, from Holyhead, Gwynedd, represented the RNLI at the service at London's Whitehall.
First Minister Carwyn Jones was among those attending the event in Cardiff, while Welsh Secretary Alun Cairns was at a ceremony at the Cenotaph in London.
Mr Jones said: "It is important we take the opportunity to pay tribute to those who lost their lives, paying the ultimate price for our freedom.
"Those who fought bravely for our futures must never be forgotten."
Among the crowd in Cardiff was couple Robert and Wendy Barnett, from Rhoose, Vale of Glamorgan, who are both former members of the armed forces.
"It's important to remember former colleagues at this time," said Mr Barnett, a former member of the Royal Logistic Corps.
For the third year, falling poppies will be projected on to Elizabeth Tower, which houses Big Ben in London, from dusk on Remembrance Sunday.
In addition, this year will see a series of war poems alongside them from the poet laureate or national poet from the four nations of the United Kingdom.
National poet of Wales, Caernarfon-based Ifor ap Glyn, will see his poem Terasau projected as part of this.
Mr Glyn said: "Terasau was inspired by a visit to the military cemeteries of the Somme, the humbling scale of loss and the near impossibility of 'knowing' the men who lie there."
On Friday, Wales fell silent on Armistice Day, which marks the ending of World War One, at the 11th hour of the 11th day of the 11th month in 1918.
The Royal British Legion's area manager for Wales, Ant Metcalfe, said: "This year marks the centenary of the Battle of the Somme, which ended on 18 November 1916.
"The impact of the battle was felt deeply in every community in Wales, particularly the casualties at the battle of Mametz Wood, where around 4,000 men from the 38th (Welsh) Division died or were injured.
"The Royal British Legion ensures the memories of those who have made the ultimate sacrifice for their country will live on."
A teenage motorcyclist was seriously injured when he came off his bike after hitting a rope tied between two trees.
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Services have been held across Wales to honour those killed in war as part of Remembrance Sunday.