This includes the cost of new protective gear for officers, as well as other funding associated with information technology and transport, according to Police Scotland.
The Scottish Government is now facing calls to increase budgets to reflect the impact of the virus.
The extra costs only relate to the first three months of the year, so are expected to rise even further when the financial impact of full lockdown during April and May are taken into account.
The figures have emerged in a submission to the Scottish Police Authority setting out the national force's financial position, ahead of a board meeting later this week.
"The quarter one forecast net cost of Covid-19 is a pressure of £4.7million, with no compensating funding from the Scottish Government," it states.
"When combined with £4.7million of one-off in-year benefits and a £1million pressure related to COP26 recruitment, the overall quarter one forecast is £1million over budget."
The £1million COP26 costs relate to the climate change conference which was earmarked to take place in Glasgow in November, but has been delayed a year.
Scottish Tory justice spokesman Liam Kerr said: "Police budgets have already been under strain due to costcutting measures from the SNP and the Covid-19 pandemic has only made those pressures even greater.
"It is time for the SNP's Justice Secretary [Humza Yousaf] to reward our officers for their work and give them an increased budget settlement."
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