The incident took place during a prayer service at the city’s Golden Temple on Saturday, according to local media.
The man allegedly barged into the inner sanctum, where Sikhism’s holy book, the Guru Granth Sahib, is kept.
He then grabbed a ceremonial sword placed next to the book, but was overpowered by guards and worshippers.
Sikhs regard the Guru Granth Sahib as not just the holy scripture of their religion but also as the living Guru, and believe it should be treated with respect as a human might be.
The scuffle took place at around 17:45 local time (11:45 GMT), and was captured on camera as evening prayers were being broadcast on television.
It is unclear exactly what happened next. Police said the man was found dead once officers arrived at the scene, and an investigation is under way.
Less than 24 hours later, another man was beaten to death by Sikhs accusing him of sacrilege after he allegedly tried to remove the Sikh flag, Nishan Sahib, from a temple in Kapurthala, also in Punjab state.
Indian media report police initially took the man into custody but locals then clashed with police and ended up killing the man.
Punjab state’s police chief tweeted that “Stern action will be taken against all those disturbing the law and order in Punjab” after the “unfortunate incidents” in Amritsar and Kapurthala.
In a tweet after the Golden Temple incident, Punjab Chief Minister Charanjit Singh Channi said he had ordered police to “zero in” on the “underlying motive and real conspirators behind this dastardly act”.
The incident comes only days after another man was apprehended for allegedly throwing a small Sikh holy book, the Gutka Sahib, into a man-made pool surrounding the temple.
The desecration of the Guru Granth Sahib is a highly emotive issue among the Sikh community.
Several desecrations took place in 2014 and 2015, and it became a major political issue during Punjab’s elections in 2017 and 2019.
The ruling Congress party has been criticised by political opponents, and many Sikhs, for failing to bring justice to previous offenders of desecrations.
Balwinder Bhunder, an MP for opposition party Akali Dal, condemned the latest incident on Saturday, telling local outlet NDTV that it was a deliberate attempt “to weaken Punjab, which is the sword arm of India”.
“Some people have made it a political game over the last five years,” he added.