Arsenal are due to play Wolverhampton Wanderers at Emirates Stadium on the Boxing Day bank holiday while Chelsea are scheduled to meet neighbours Fulham at Stamford Bridge in the capital's other Premier League match.
The strike could also affect lower division games with the Championship matches between Watford and Cardiff City and Millwall and Portsmouth also under threat.
Leyton Orient's match with MK Dons and Brentford's clash with Bournemouth in League One, as well as the League Two fixtures between AFC Wimbledon and Oxford United and Dagenham & Redbridge and Barnet could also be postponed.
In a statement Arsenal said: "We are closely monitoring the situation together with all the relevant agencies including the Metropolitan Police, Transport for London, London Underground, The Premier League, Wolverhampton Wanderers FC and Islington Council.
"The paramount concern to Arsenal Football Club is the duty of care we have towards the Arsenal supporters, Wolverhampton Wanderers supporters, matchday employees and indeed everyone who is planning to attend this match."
The planned strike is the result of a dispute over workers' bank holiday pay but the legality of the walkout has been challenged by the transport authorities and will be decided in the High Court in London on Wednesday.
