The charity said this was disproportionate to the sector's size, which is 13% of housing in Scotland.
Homeless applications have decreased by a third in the past five years but the Shelter said the statistics did not tell the full story.
It said it was important that vulnerable households were supported before they were pushed into crisis.
According to the latest Scottish government figures, the proportion of  homeless applications that come from the private rental tenants rose from 13% 2008-09 to 18% in 2013-14.
However overall homelessness in Scotland fell by 34% during the same period, official statistics showed.
Graeme Brown, director of Shelter Scotland, said: "Whilst the headline figures show that homelessness applications are down by one third in the last five years, which is welcome, our analysis shows it is not all good news for homeless people in Scotland.
"The 36,457 households making homeless applications, a youth homelessness rate at 13.7 per 1,000 and a rising proportion of homeless applications from the private rented sector signal that, although there are movements in the right direction, there is still a long way to go."
"With the significant weakening of the welfare state in recent years, it is more important than ever to ensure that vulnerable households are offered support before they are pushed into crisis."
The report, 'Homelessness in Scotland 2014: Getting Behind the Statistics', has been released ahead of Shelter Scotland's annual conference later this month.
Housing minister Margaret Burgess said: "Homelessness in Scotland is falling and the number of homeless applications from the private rented sector has actually fallen by 21% since 2008/09.
"The Scottish government is working closely with local authorities and their partners, and with Shelter, to prevent homelessness, increase the number of affordable homes and address the issue of empty homes. Where people do become homeless, our focus is on finding the best outcomes."

The Mediterranean gull and black-headed gull eggs were illegally harvested from from islands in Poole Harbour, Dorset.
The theft has been branded "sickening" by bird charity Birds of Poole Harbour.
The group said some eggs - sometimes eaten as a delicacy - were not cleared for human consumption.
Dorset Police and Natural England have launched an investigation.
Natural England is urging any restaurants or pubs to ask to see a valid licence before buying eggs to prepare in meals.
Birds of Poole Harbour had been surveying a group of islands in the harbour when the theft was discovered.
Mediterranean gulls are classified as a Schedule One species, meaning anyone disturbing their nests must have a special licence.
Paul Morton, who runs the charity, said Mediterranean gulls' eggs were not approved for human consumption, and could be a "health issue".
"I'm distraught, really. To see the taking of hundreds and hundreds of eggs from an important colony is quite sickening," he said.
Mr Moreton said there had been previous convictions for egg poaching in the last 10 or 15 years.
He said continued monitoring was needed to understand the effect on the gull population in the harbour, which he said had fallen by 70% since 2008.
Almost a fifth of homeless applications now come from the private rented sector, according to Shelter Scotland.
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Hundreds of eggs belonging to a protected species of bird have been stolen from an important nesting site, with fears they could be sold to the restaurant industry.