Rachel Booth was at the rally on 11 June in Manchester, which organisers said was "against Islamic hate".
She said she attended in sympathy for the victims of the Manchester attack that killed 22 people on 22 May.
Moor Nook Primary School, in Preston, confirmed a member of staff has been suspended "pending further inquiries".
Thousands of people attended the march by a coalition that calls itself UK Against Hate, held three weeks after a suicide bombing at an Ariana Grande concert.
The rally also drew hundreds of people in a counter-demonstration against the march.
Mrs Booth, who has worked at the school for four years, said the suspension was "a big shock".
"I have never been in any kind of trouble with police.
"The grounds for suspending me are it was an EDL march, which is a load of rubbish. Even if I was part of the EDL, which I'm certainly not, it should not have affected my job."
She said she attended with her mixed race husband, who is a former serviceman, to show solidarity with the bombing victims, not to support far-right extremism.
"I thought it was for the children and so I went," she added.
The march was criticised at the time by Greater Manchester Mayor Andy Burnham who tweeted: "These EDL-types who came today need to have a look at themselves."
In a letter to the school, Mohammed Fyaz, one of the march's organisers, wrote "the event in question was not organised by or linked to the EDL in any way".
He added: "In the democracy in which we live political, religious and moral issues should be allowed to be discussed, questioned and at times challenged freely, without fear of persecution or discrimination."
It is understood a suspension in such circumstances is a "neutral" act and will allow the school to investigate footage from the march featuring Mrs Booth.

Mr Farron was quoted in the Mail on Sunday suggesting that the Lib Dem brand would be tainted for a generation by governing with the Conservatives.
Lord Ashdown said: "Tim's a very able guy but at the moment judgement is not his strong suit."
He was asked about Mr Farron's comments on Radio 5 Live's Pienaar's Politics.
The Lib Dem election campaign chief, and former leader, went on to say: "I know Tim very well. He is a great campaigner, a good friend of mine. I think his well-known ambitions would probably be better served with a little more patience and a little more judgement."
Mr Farron was quoted as saying: "In 2010, many people said: I am not voting for you because of the Lib Lab pact (in the 1970s) when I was seven years old. Just think what going into coalition with the Tories will do to our brand over the next generation."
The Lib Dems insist that was not a new quote.
A primary school dinner lady who attended a march co-organised by former English Defence League (EDL) leader Tommy Robinson has been suspended.
[NEXT_CONCEPT]
Lord Ashdown has said Tim Farron - one of the frontrunners to be a future Liberal Democrat leader - lacks judgement.