Rail union RMT said its members would not work on from Sunday 30 September to Monday 1 October.
RMT said working conditions at Eurostar were "shocking and dangerous" because of repeated service failures and breakdowns.
"The international terminal at St Pancras has been reduced to chaos, with staff left to bear the brunt of public anger, following a spate of service problems that dumped thousands of passengers on the cramped concourse at St Pancras as the season headed towards its summer peak," it said. "RMT has repeatedly demanded action to improve conditions but with nothing tangible coming from Eurostar there is no option but to strike.
RMT general secretary Mick Cash said the union "remains available for genuine and serious talks that will bring about guarantees to resolve the situation.”
Eurostar connects London to hotspot destinations in Europe such as Amsterdam, Brussels, Paris and Rotterdam through the Channel Tunnel, which is operated by Getlink.
Over the summer it suffered a number of strikes from the RMT over disrupted services.
A Eurostar spokesperson said: “We are aware of the proposed strike and are disappointed that this action is planned. We are meeting with the RMT next week to discuss this further and hope to find a solution.”