Its study found many of the most vulnerable in society struggle to access the internet or complete online forms.
It said people will be denied access to jobs and benefits unless there is a rethink of the plans.
The UK Government will replace Jobseeker's Allowance, Employment and Support Allowance, Housing Benefit, Income Support and tax credits with the new Universal Credit from October this year.
The new benefit will be rolled out gradually and is expected to be fully in place by 2017, with around 700,000 Scots households affected.
Ministers said all claims must be processed online, and claims by telephone or through face-to-face-contact will only be done in exceptional circumstances.
CAS spokeswoman Sarah Beattie-Smith said the UK Government's digital strategy should be based on support and encouragement rather than compulsion.
She said: "People who are entitled to benefits should be able to access them in a way which suits their needs, resources and capabilities. And benefit claimants and jobseekers who don't have the skills or access to use the internet must not be penalised for this.
"Rather, Jobcentres should support people to gain those skills and find work, and more broadly the Government has a duty to support the roll-out of internet access to all parts of the country.
"When it comes to jobseekers, surely it makes sense to let people use every means possible to find work, and not constrain them in any way."
Problems accessing the internet are particularly prevalent in Glasgow, where a recent report by communications watchdog Ofcom found only 53% had access to broadband.
Scotland's largest city struggles with high levels of unemployment, and recorded the largest number of claimants in Scotland in December last year.
Overall, 15% of Scots told Ofcom they have no access to the internet due to the cost of line rental and maintaining a PC – the highest figure in the country.
The plan's critics claim this was not being taken into account by the Government, with Ian Tasker, assistant secretary of the Scottish Trades Union Congress, saying: "We share Citizen's Advice Scotland's concerns.
"Statistics show that fewer people in Scotland have access to the internet than other part of the UK."
The CAS study found that other benefits are already being restricted because of a push towards digital services, with a number of first-hand accounts included in the report outlining problems faced by people with little experience of computers.
One 60-year-old with no IT skills was threatened with sanctions for not looking for work as he had not applied for jobs online, while another was told he must apply for work through the internet despite being dyslexic.
The Department for Work and Pensions runs pilot schemes to support people using digital channels to claim benefits in Dumfries and Galloway, North Lanarkshire and West Dunbartonshire.
A spokesman said: "It makes sense that our services are designed to prepare people for the world of work. Around 78% of working age benefit claimants already use the internet, 48% of those say they log on every day, many to search for jobs online.
"We've always recognised that some people will need extra support to access the internet and so in preparing for Universal Credit we are working with local authorities and local services to determine who will need this extra help – be it money advice services, face to face support or help to get online - and how best to deliver it."
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