The product, Virapro Hand Sanitiser (PCS 100409), is used in many schools by students and staff.
The department warned that prolonged use of the sanitiser may cause dermatitis, eye irritation, upper respiratory system irritation and headaches.
It removed the product from the Biocidal Product Register because of the public health concerns.
On Thursday, members of the public were urged not to use the product as it contains methanol rather than ethanol.
On Friday night, the department said, in the course of the investigation into the hand sanitiser, it emerged that a number of other sanitary products under the Virapro brand were not on its approved list for biocidal products.
“The company concerned has been advised to withdraw all of these products from the market,” said a departmental statement.
“The department is therefore advising, on a precautionary basis, that all sanitary products in the Virapro range should be returned to the supplier.
“Members of the public are advised to stop using these products because they are not authorised for use.”
The department said all products containing biocides were required to have specific information and data on the labels.
Important message below, as sent on Aladdin pic.twitter.com/MZdjI9lXiS
— St.Patrick's BNS (@saintpatsbns) October 22, 2020
A number of schools were forced to shut their doors on Friday amid the hand sanitiser scare.
St Patrick’s Boys National School in Drumcondra and Gaelscoil Ros Eo in Rush were among the schools to close for the day.
Professor Anne Looney, chairwoman of St Patrick’s Boys school, said pupils were disappointed as Friday was fancy dress day.
She told the Today with Claire Byrne show that she searched shops online to purchase sanitiser late on Thursday night.
“I knew that probably local schools would be able to help,” she added.
“They’d been in touch this morning but there was too much uncertainty and this was actually dress-up day in school, so there was a slightly higher level of risk and the importance of having the sanitiser in place for every boy and every staff member coming in, so getting that certainty – we couldn’t give that.
“Then on balance given the level of risk and the need to give certainty we made the decision to close.”
Sinn Fein’s education spokesman Donnchadh O Laoghaire said that school principals were left to make last-minute decisions on Friday morning.
“Schools have been through an incredible year, the stress and the strain they felt.
“The last thing that they needed, less than two days from the mid-term break, was a notification from the Minister for Education at 10.40pm saying that this particular hand sanitiser was not suitable for use,” he added.
“A lot of principals and schools wouldn’t have seen that until this morning, they would have to make a split decision on a really tight timeframe with massive implications.
“I’ve had emails from parents who said their schools had no other choice and that causes its own difficulties for parents having to take the day off or look for childcare.
“The issue is communication here, this was due to be recalled by the Department of Agriculture on Tuesday last.
“Did the Department of Agriculture not tell the Department of Education or did the Department of Education not get the word out in time?”
Dr Paddy Mallon, consultant in infectious disease at St Vincent’s Hospital in Dublin, said the incident was “surprising”.
“Whether it’s schools or hospitals, everyone has been struggling to access sufficient supplies of what we need but that has improved over time,” he added.
“We need to recognise that there is a need to focus on safety but also how important hand sanitiser and hand washing is.
“It’s an unfortunate hiccup that has had a severe impact on schools.
“The majority of hand sanitiser won’t have this particular type of alcohol.
“We need to continue to be diligent and frequent users of hand sanitisers because it is key in protecting ourselves.”
