A special bench of three judges threw out the petition within moments of opening the case and without allowing any testimony.
The petition was first launched 28 years ago and triggered countrywide protests.
“We are saddened (at the ruling),” said Subrata Chowdhury, who represented the secular activists in the case.
Bangladesh was declared officially secular after the 1971 war of independence from Pakistan which created the nation from what was previously East Pakistan.
In 1988 the then-military ruler, General Hussain Muhammad Ershad, elevated Islam to the state religion.
Secularists have argued for decades that having Islam as the state religion conflicts with Bangladesh’s secular charter and discriminates against non-Muslims.
More than 90 percent of Bangladesh’s population is Muslim, with Hindus and Buddhists the main minorities.
One of the country’s party, Jamaat-e-Islami, responded to the court’s decision by withdrawing a call for a nationwide strike. It described the outcome as a “victory of 160 million people”.
Hefazat-e-Islam, a political group also welcomed the court’s move.
“We thank the high court for rescuing the country from a massive disaster,” Hefazat’s organising secretary Azizul Hoque Islamabadi told media.
Some 7,000 activists had taken to the streets of the capital Dhaka after prayers last Friday, chanting anti-government slogans and holding banners to protest against the high court’s move to hear the plea.
Bangladesh has been plagued by unrest in the last three years and experts say a long-running political crisis has radicalised opponents of the government.
The secular government launched a nationwide crackdown on Jamaat in 2013, detaining or prosecuting tens of thousands of activists.
A controversial war crimes tribunal has ordered the execution of several top Jamaat leaders, dividing the country and sparking deadly protests.
Constitutional changes dating back over three decades have put Bangladesh in the unusual position of being officially secular while still having Islam as a state religion.
Hasina’s government has brought back secularism as a pillar of the constitution, but promised it would not ratify any laws that go against the central tenets of Islam.
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