Phone lines to Naypyitaw, the capital, were not reachable in the early hours of Monday. Parliament had been due to start sitting there on Monday after a November election the NLD had won in a landslide.
A military spokesman did not answer phone calls seeking comment.
State-run MRTV television said in a Facebook post that it was unable to broadcast due to technical issues.
An NLD lawmaker, who asked not to be named for fear of retaliation, said another of those detained was Han Thar Myint, a member of the party’s central executive committee.
Nobel Peace Prize winner Suu Kyi, 75, came to power after a 2015 landslide election win that followed decades of house arrest in a struggle for democracy that turned her into an international icon.
Her international standing was damaged after hundreds of thousands of Rohingya fled army operations into refuge from Myanmar’s western Rakhine state in 2017, but she remains hugely popular at home.
The NLD won a landslide in last November’s election, hammering a pro-military party.
Myanmar’s military had said on Saturday it would protect and abide by the constitution and act according to law after comments earlier in the week had raised fears of a coup.
Myanmar’s election commission has rejected the military’s allegations of vote fraud, saying there were no errors big enough to affect the credibility of the vote.