The army admitted it had carried out the detentions in response to "election fraud," handing power to military chief Min Aung Hlaing and imposing a state of emergency for one year, according to a statement on a military-owned television station.
Suu Kyi's party published comments on Facebook that it claims had been written in anticipation of a coup, quoting her as saying people should protest against the military takeover.
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The coup derails years of Western-backed efforts to establish democracy in Myanmar, where neighboring China also has a powerful influence.
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The generals made their move hours before parliament had been set to sit for the first time since the NLD's landslide win in a Nov. 8 general election viewed as a referendum on Suu Kyi's fledgling democratic rule.
Phone and internet connections in the capital, Naypyidaw, and the main commercial center of Yangon were disrupted and state television went off air after the NLD leaders were detained.
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NLD leaders were "taken" in the early hours of the morning, NLD spokesman Myo Nyunt told Reuters on a phone conference.
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A video posted to Facebook by one MP appeared to show the arrest of another, regional lawmaker Pa Pa Han.
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In the video, her husband pleads with men in military garb standing outside the gate. A young child can be seen clinging to his chest and wailing.
Troops and riot police stood by in Yangon where residents rushed to markets to stock up on supplies and others lined up at ATMs to withdraw cash. Banks subsequently suspended services due to poor internet connections.
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The detentions came after days of escalating tension between the civilian government and the military in the aftermath of the election.
The pre-written statement uploaded on an NLD Facebook page quoted Suu Kyi as saying such army actions would put Myanmar "back under a dictatorship."
"I urge people not to accept this, to respond and wholeheartedly to protest against the coup by the military," it quoted her.
Supporters of the military celebrated the coup, parading through Yangon in pickup trucks and waving national flags.
"Today is the day that people are happy," one nationalist monk told a cheering crowd in a video published on Facebook.
But democracy activists and NLD voters were horrified and angry.
"Our country was a bird that was just learning to fly. Now the army broke our wings,” student activist Si Thu Tun stressed.
"The NLD is the government we voted for. If they're unhappy with the result, they can call another election. A coup isn't acceptable," said a woman, who declined to be identified, whose husband works for the military.
"Unless this problem is resolved, it will obstruct the path to democracy and it must therefore be resolved according to the law," the military said.
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