The council announced the cash will be available to minimise the impact of the virus on its communities and council services, with an emphasis on health and social care funding.
Latest figures show that 60 cases of Covid-19 have been confirmed in Scotland – up from 24 on Wednesday – with 11 in the NHS Lothian area in which Edinburgh sits.
Council leader Adam McVey said in a statement: “We and our partners are working round the clock to ensure Edinburgh is ready for however the coronavirus situation develops in the days, weeks and months ahead.
“It is a worrying and uncertain time for everyone and today we’ve confirmed an immediate allocation of £2m to reinforce the proactive and preventative measures we’ll need to take.”
The council said it would send relevant information to for its staff, and to schools, and update the public on a dedicated web page.
McVey said: “This is a very challenging time for the city, and the world, but if we all pull together I know we will get through it.”
Edinburgh was allocated £7.43m in additional funding in the Scottish Government’s budget at the end of February after a deal struck between the SNP and Scottish Green Party.
Earlier this week, UK chancellor Rishi Sunak unveiled a £12bn funding package to tackle impacts from the coronavirus, including business rate exemptions for small businesses in England.
