The slip has resulted in a perimeter fence lying horizontal over the banking with very little to retain it and the roots of a nearby tree have also been exposed.
The fear is that any further ground disturbance could cause this tree to fall.
Scottish Borders Council have put markers and warning signs in place where the slip happened, close to a route popular with walkers.
This is the third landslip in the Lennel area in the last few years; the two previous ones being attributed to excess surface water and a burst sewage pipe.
But this time around the cause isn't as easily identifiable, although Lennel resident and Coldstream Community Council member, David Tait, one of the first to be alerted to the most recent slip last month, said the extreme conditions a few months ago can't have helped.
Speaking to 'The Berwickshire News' earlier this week he said: "It's quite a large bit of land that's come away, maybe the size of a house I would say and it's encroaching on some of the graves.
"Unlike the other occasions where the landslips were blamed on surface water and sewage, my opinion is that this one has a lot to do with the weather earlier in the year.
"I remember it well because I was lambing at the time. I've still got marked in my diary that on March 30 and 31 we had torrential rainfall and gale force winds.
"At the same time there was heavy snowfall in Duns but for every two inches of snow they got, we got an inch of rain. A great deal fell in the space of one week.
"And when the weather starts to dry up and it gets a bit warmer cracks start appearing in the soil which can cause erosion."
David said that the worst case scenario for the people of Lennel would be if there was repeat of the weather of August 2008, which caused chaos for Civic Week campers on Tweed Green.
He continued: "Everyone in the village is dreading another spell of persistent heavy rain like two years ago.
"Another flash flood and more land is likely to come away and take debris with it into the Tweed.
"At present the public walkaway is still open but I certainly wouldn't walk along there, especially not in the dark.
"It's quite a steep bank- lose your footing and you'd be in trouble."
The matter has been discussed at a meeting of the Coldstream and District Community Council and chairman Martin Brims said that their concern was the potential for any further landslips and the effect they could have on the whole cemetry.
He commented: "It's obvious to everyone that some of the burial plots are extremely close to where the landslip happened.
"Without wanting to sound too dramatic, if there is any further disturbance there is a realistic possibility that some of the gravestones could get sucked into 'the danger zone'.
"This is a big concern for us. Most of the graves in the cemetery are quite aged but this doesn't lessen the impact for people's relatives should the situation get worse.
"The primary focus for us as a community council was to report the matter to our local councillors. I haven't got the professional expertise to even begin to speculate what caused the landslip but at this stage, from what I have been told by Councillor Trevor Jones, I am satisfied that Scottish Borders Council are dealing with this issue and are exploring options for remediation."
Councillor Jones added: "After having visited the cemetery myself I wouldn't say there were any graves in immediate danger.
"I wouldn't want to cause anyone any unnecessary alarm.
"I'm quite happy with how the council have dealt with the situation thus far.
"As you'd expect they are taking it seriously and have put up markers and warning signs which they are designated to provide."
A council spokesperson said there were a number of issues which needed to be resolved regarding the ownership of the affected land, adding that it could be "a drawn out process".