News of Shinawatra emerged as opposition to the army's takeover grew among her supporters and pro-democracy activists.
Hague said: "There should never be recourse to violence. Only by openly discussing the full range of issues can Thailand move forward and reach a more stable position," he said.
The army moved on Thursday after failing to forge a compromise in a power struggle between Yingluck's populist government and the royalist establishment, which brought months of sometimes violent unrest to Bangkok's streets.
The military detained Yingluck on Friday when she and scores of other people, most of them political associates, were summoned to an army facility in Bangkok. More people have been summoned this weekend, including some academics.
A senior officer said Yingluck could be held for up to a week and Thai media reported she had been taken to an army base in Saraburi province north of Bangkok, but an aide to Shinawatra denied that.
"Now she's in a safe place ... She has not been detained in any military camp. That's all I can say at this moment," the aide said, declining to be identified.
A source from her Puea Thai Party added: "We can't say she is absolutely free because there are soldiers in the area, monitoring her."
This source said several former ministers from her cabinet were being held in army facilities in Saraburi.
Army deputy spokesman Winthai Suvaree told a news conference that anyone being held would not be detained for more than seven days. He did not mention Yingluck.
Thailand's political woes are the latest chapter in a nearly decade-long clash between the Bangkok-based establishment and Thaksin Shinawatra, the brother of Yingluck. Thaksin is a former telecommunications tycoon who broke the mould of Thai politics with pro-poor policies that won him huge support and repeated electoral victories.
Thaksin was ousted in a 2006 coup and left the country after a 2008 graft conviction, but he remains Thailand's most influential politician and was the guiding hand behind the government of Yingluck. The Shinawatras' populist movement has won every national election since 2001 but Thaksin now lives in self-imposed exile to avoid corruption charges. However, he still wields enormous influence over Thailand's political affairs and remains at the heart of the crisis. Despite international calls for the restoration of democratic government, army chief General Prayuth Chan-ocha has not promised a swift return to civilian rule, insisting there must be broad reforms and stability first.
"We must have economic, social and political reforms before elections," Prayuth told hundreds of civil servants on Friday in his first comments on his plans since the coup. "If the situation is peaceful, we are ready to return power to the people," he added.
But reforms could take many months and stability could be elusive. Human Rights Watch said rights in Thailand were in "free fall".
General Prayuth also said paying farmers money they were owed under a failed subsidy scheme organised by Yingluck's government was "an urgent issue".
The military has banned gatherings of more than five people, censored the media and imposed a 10pm to 5am curfew, but that has not stopped some people from showing their disapproval.
About 200 people gathered at a mall and entertainment complex in northern Bangkok on Saturday, holding up handwritten slogans such as "Anti the Coup".
Police tried to move them on, but they were shouted down and retreated.
The crowd, with young men on motorcycles leading the way, then tried to move south to the Victory Monument roundabout, but police lined up across the road to block them. There was some pushing and some plastic water bottles were thrown, but no major violence or injuries. Several hundred people, including students, also gathered in a central Bangkok shopping district until soldiers dispersed them. A small crowd staged a protest in the northern city of Chiang Mai, Thaksin's hometown.
The real danger for the military would be a sustained mass campaign by Thaksin's "red shirt" loyalists.
Thaksin's supporters in his northern and northeastern heartlands have repeatedly said they would act if another pro-Thaksin government was forced from power unconstitutionally. Thaksin has not commented publicly since the coup.
A resolute, well-financed campaign by Thaksin's red shirts, whose ranks include armed activists, would be a major test for the military. The use of force to put down protesters could squander any legitimacy the military leaders may have after saying they took power in the first place to end violence and restore order. A 2010 crackdown on Thaksin's supporters ended in serious bloodshed and damage to the army's image. Just over a year later a pro-Thaksin government was back in power after Yingluck's sweeping election victory.
Yesterday, US secretary of state John Kerry condemned the takeover and warned it would "have negative implications for the US-Thai relationship", but did not announce immediate punitive steps. The State Department said it was reviewing millions of pounds in aid.