They said some work on the three-mile route from York Place in the city centre would be “re-sequenced” in an attempt to minimise any impact on the scheme.
It will also mean “critical” areas will be prioritised until supplies increase.
Edinburgh City Council admitted the shortage could delay or increase the cost of other projects.
Its latest update on the tram line extension stated: “A nationwide industry issue with the supply of concrete and other materials is impacting not only on trams to Newhaven, but construction projects across the country.
"The project team continues to work on mitigation measures, including re-sequencing of works, to minimise any impact.
"This may result in some sites seeing a reduced level of progress while we prioritise programme critical areas during the supply shortage period.
“The project is still on course for completion by spring 2023 and within budget.”
Areas where concrete is still required includes Ocean Drive, Constitution Street, and Leith Walk near McDonald Road.
Construction of the extension started in November 2019, five years after the original nine-mile line opened between Edinburgh Airport and York Place.
A spokesperson for Edinburgh City Council, which is in charge of the project, said: “We continue to work towards a spring 2023 date for a revenue service being operational, and so are working with our contractor on a number of mitigation measures to allow us to stay on programme.
"In the meantime, there may be less activity than usual in some worksites.”
However, the spokesperson said some of its other projects could be delayed.
They said: "The impact is likely to vary from project to project, but there is a risk that some may be delayed or experience cost pressures.
"We’ve rightly factored this in our project risk management calculations for all our construction projects and will continue to monitor the situation closely.”
Institution of Civil Engineers Scotland director Hannah Smith said: “We are aware of reports from members noting their businesses are experiencing significant issues which impacts on delivery programmes, costs and tendering.
“Clearly this is concerning as effective infrastructure delivery is at the heart of supporting economic recovery, tackling climate change and developing the future workforce.”
The Scottish Government’s Transport Scotland agency, which is responsible for major projects such as the £3 billion A9 dualling between Perth and Inverness, said it had also taken action in an attempt to offset any impacts.
Its spokesperson said: “A year of challenging supply chain conditions, EU exit uncertainty and Covid-19 pandemic impacts on the wider economy and workforce, is resulting in a number of supply chain issues being experienced in a range of areas.
“Since the end of 2020, there have been significant increases in demand for construction materials compared to normal levels.
"Shortages have been reported in the UK and Scotland across a range of materials, including timber, steel, roofing products and cement.
“Transport Scotland continues to pro-actively monitor the market and supply chain and engage with our suppliers and industry partners to consider mechanisms and processes under our contracts and for our procurements to try to mitigate the effects and risks arising from any shortages.”