Harry Kane and Gareth Bale had planned to wear the armbands, which promote inclusivity, in their respective games against Iran and the USA.
However, they are among seven European nations who decided at the last minute not to wear the armbands for fear of sporting sanctions from Fifa.
World football's governing body had threatened the captains with yellow cards if they wore the armbands.
A joint statement from the football associations of England, Wales, the Netherlands, Belgium, Denmark, Germany and Switzerland read: "Fifa has been very clear that it will impose sporting sanctions if our captains wear the armbands on the field of play.
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"As national federations, we can’t put our players in a position where they could face sporting sanctions including bookings, so we have asked the captains not to attempt to wear the armbands in Fifa World Cup games.
"We were prepared to pay fines that would normally apply to breaches of kit regulations and had a strong commitment to wearing the armband. However, we cannot put our players in the situation where they might be booked or even forced to leave the field of play."
England kick off their 2022 World Cup campaign in Qatar against Iran at lunchtime, while Monday's other match in Group B is Wales versus the USA later in the evening.
The OneLove campaign aims to "promote inclusion and send a message against discrimination of any kind".
In Qatar, homosexuality is illegal and anyone found participating in same-sex sexual activity can be punished by up to seven years in prison.
What is the OneLove armband and what does it mean?
The heart-shaped multi-coloured armband with a 1 in the middle, worn by the captains of several European international football teams, is part of the OneLove campaign to promote inclusivity and LGBTQ+ rights.
While the armbands do not directly reference Qatar's controversial anti-LGBTQ+ laws, they are seen as a strong symbol in a World Cup that was highly criticised before a ball was even kicked in its opening game on Sunday.
Who started the campaign?
The OneLove initiative was launched by the football association of the Netherlands, whose captain wore the armband in last year's delayed Euro 2020 tournament.
The armbands have been worn in a number of Nations League matches between European countries, with government body Uefa's permission.
Why is the armband controversial for Fifa and Qatar?
World Cup rules state that captains must wear armbands provided by Fifa, which has its own for group games and the knockout stage, ranging in themes such as "save the planet", "protect children", "share the meal" and even "no discrimination", despite Qatari laws discriminating against gay people.
Fifa does not allow the use of slogans or political messages on kits during the World Cup.
‘No discrimination’ had been due to be the theme for the quarter-finals but the global governing body confirmed on Monday, within seconds of the joint football associations’ statement, that it had been brought forward.
The statement also reminded teams that “For Fifa final competitions, the captain of each team must wear the captain’s armband provided by Fifa.”
Since it was announced as hosts of the tournament, Qatar has been criticised for its human rights record, particularly its treatment of migrant workers and LGBTQ+ people.
Why was the decision left so late?
The FA wrote to Fifa in September to request permission to wear the OneLove armband, but received no response.
In their joint statement, the seven European football associations said: "We are very frustrated by the Fifa decision which we believe is unprecedented.
"We wrote to Fifa in September informing them of our wish to wear the OneLove armband to actively support inclusion in football, and had no response.
"Our players and coaches are disappointed – they are strong supporters of inclusion and will show support in other ways."
Kane had said previously: “We’ve made it clear as a team and a staff and organisation that we want to wear the armband. I think we’ve made it clear that we want to wear it.”
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