A close friend said the 64-year-old campaigned to stand up against poverty, corruption and inequality.
Mr Juarez was murdered on Thursday outside his hotel in Ocampo in the southwestern state of Michoacan. Video of the detention aired by local media showed uniformed officers hitting each other as gunshots go off in the background.
Telesur reports that that after Suarez and his wife were shot dead outside a hotel, federal police tried to arrest Garcia, the public security secretary, on Saturday, but were blocked by the 27 officers under his command.
The security secretariat said: "All of them are being interviewed to proceed as due under law in the event anyone has taken part in acts that violate the town's codes".
At least 18 candidates have been killed while running for some type of political post across Mexico, nearly all of them running for a local position.
"He couldn't stand seeing so much poverty, inequality and corruption and so he made a decision to run", one of his closest friends, Miguel Malagón, told El Universal.
Next Sunday, Mexico will hold presidential elections, with more than 3,400 positions on state and municipal levels being up for grabs across the country.
The 2018 election campaign has been the bloodiest in Mexico's modern history with dozens of politicians, candidates and activists murdered by criminal groups and gangsters seeking to influence the shape of the post-electoral map.
The electorate will be voting for a new president, as well as for federal, state and municipal posts.