Jagdish Singh said it was "troubling" to find out that tallow - derived from beef or mutton, but sometimes pork - was used to manufacture the fiver.
He joined a number of Hindus in urging the notes be banned from temples, where meat products are forbidden.
A petition to ban the new £5 notes has attracted more than 100,000 signatures.
It calls on the Bank of England to "cease to use animal products in the production of currency that we have to use".
Hosted on the Change.org website, it states that tallow is "unacceptable to millions of vegans, vegetarians, Hindus, Sikhs, Jains and others in the UK".
The Bank of England began issuing the polymer notes in September pledging they "last longer, stay cleaner and are harder to counterfeit than paper notes".
Its only response so far to the petition has been in a statement to "confirm that the polymer pellet from which the base substrate is made contains a trace of a substance known as tallow".
Critics say there are plant-based substitutes that could be used in its place.
The response from the UK's Hindu and Sikh communities began to gather pace after vegans and vegetarians voiced their feelings on social media on Tuesday.
Hindus believe cows are holy and sacred, and many do not wear shoes or carry bags made from the skin of cattle that has been slaughtered. Practising Sikhs are strict vegetarians.
Speaking to the BBC's Asian Network, Coventry-based Mr Singh said: "Every time I come across a £5 note I'll be reminded that it contains meat by-product."
He said no animal by-product should breach the sanctity of a gurdwara [Sikh temple].
Gauri Das, managing director at the Bhaktivedanta Manor Hindu temple in Watford, is calling for the notes to be banned from his site immediately.
"Our temples prosper on the charity of all of our members," he said.
"Our ethos is not to harm animals. It's problematic for us because we're implicated in the process. So it's immediately become a matter of concern for our community."
Meanwhile, the president of one of the largest Hindu temples in Leicester has urged worshippers not to give charitable donations with the new £5.
Vibhooti Acharya, from the Shree Sanatan Mandir temple, said it was a "matter of choice" but it would be putting up notices to make the community aware of the situation.
She added: "There needs to be a decision made between committee as to whether we accept £5 notes in religious ceremonies in future."

The Super Eagles have been without a permanent coach since Sunday Oliseh quit the post in February.
The Nigerian Football Federation is hoping to be able to draw up a shortlist of candidates by Friday.
"We encourage applications from all highly-qualified persons, whether they be Nigerians or expatriates," it said.
"Applications are welcome until Wednesday, and the Technical and Development Committee will meet on Friday to look through all applications and release a shortlist."
Caretaker manager Salisu Yusuf guided Nigeria to victories over Mali and Luxembourg in two friendly matches in May, but the NFF president Amaju Pinnick has publicly declared his intention to appoint a foreign manager for the country instead.
Nigeria were rocked by Oliseh's exit, brought about by a dispute over contract violations, and they had to play two crucial Africa Cup of Nations qualifiers against Egypt in March under the temporary charge of Under-23 coach Samson Siasia.
The three-time African champions were eliminated from the competition and will not feature at next year's finals in Gabon.
Opinions are sharply divided about what direction the NFF should follow after the country's failure to qualify for the 2015 and 2017 Nations Cup tournaments under local managers.
Nigeria have been drawn in the same African 2018 World Cup qualifying group B as former champions Cameroon, Algeria and Zambia.
The group includes three of the five African countries who went to the last World Cup in Brazil and they will be battling for a single place at the tournament in Russia.
Algeria and Nigeria both got past the group phase in 2014 and were eliminated in the round of 16 while Cameroon, hampered before arriving in Brazil by a player strike over money, lost all three games and conceded nine goals.
The revelation the UK's new plastic £5 note contains a small amount of animal fat is "extremely offensive", a Sikh activist has said.
[NEXT_CONCEPT]
Nigeria have started the process of finding a new manager of the national team, according to the country's football federation.