A special bench of three judges threw out the petition within moments of opening the case and without allowing any testimony, an AFP correspondent at the court said.
Bangladesh may drop Islam as country's official religion
The petition, which was first launched 28 years ago, has triggered countrywide protests by Islamist groups in the impoverished nation.
"We are saddened (at the ruling). It's a sad day for the minorities of Bangladesh," said Subrata Chowdhury, who represented the secular activists in the case.
The court did not allow the petitioners to state their case or present any arguments, he said. "The judges simply said the rule is discharged."
Bangladesh was declared officially secular after the 1971 war of independence from Pakistan which created the nation from what was previously East Pakistan.
Threats as Bangladesh mulls scrapping Islam as state religion
But in 1988 the then-military ruler, General Hussain Muhammad Ershad, elevated Islam to the state religion in an attempt to consolidate power.
Secularists have argued for decades that Islam's status as the state religion conflicts with Bangladesh's secular charter and discriminates against non-Muslims.
The government of Prime Minister Sheikh Hasina 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.
The country's largest Islamist party, Jamaat-e-Islami, responded to the court's decision by withdrawing a call for a nationwide strike. It described the decision as a "victory of 160 million people".
"The people will never accept any government move to remove Islam as the state religion from the constitution in an effort to please a handful of anti-religion persons," the Jamaat had said earlier.
More than 90 percent of Bangladesh's population is Muslim, with Hindus and Buddhists the main minorities.
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.
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 Muslims protest call to scrap state religion
The court's decision to throw it out threatens to heighten tensions between secularists and hardliners in the conservative nation, which has recently seen a spate of killings of atheist bloggers, religious minorities and foreigners.
Bangladesh's 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 Jamat leaders, a move that has divided the country and sparked deadly protests.
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