Yingluck Shinawatra is one of more than 100 political figures summoned by the army.
The army has banned 155 prominent political figures from leaving the country without permission.
On Thursday the military suspended the constitution, banned gatherings and detained politicians, saying order was needed after months of turmoil.
On Friday afternoon it appeared Yingluck Shianwatra had left the location where she had been summoned and was going to another military location.
Some pro-government lawmakers have now gone into hiding.
The coup, which followed months of anti-government protests, has drawn widespread international criticism.
It came two days after the army declared martial law.
US Secretary of State John Kerry said there was “no justification” for the coup, adding that $10 million in bilateral aid could be suspended.
The UN urged a “prompt return to constitutional, civilian, democratic rule”.
Thais, meanwhile, spent the night under a curfew which ran from 22:00 to 05:00. Bangkok was reported to be largely peaceful.
The anti-government movement has claimed victory and sent its supporters home.
Military leader General Prayuth Chan-Ocha – who has appointed himself the new prime minister – said troops were taking power “in order for the country to return to normal quickly”.
“All Thais must remain calm and government officials must work as normal,” he said in a televised address.
Political factions had been holding talks for two days. As soon as the coup was announced, several key figures were detained.
The military then issued a bulletin spelling out the key points of the takeover:
Thailand’s army, which has staged at least 12 coups since the end of the absolute monarchy in 1932, acted after months of political deadlock.
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