Kanter, who arrived in Bucharest from Jakarta, Indonesia, as part of his 2017 Enes Kanter Light Foundation global tour, posted a video on Twitter in which police officers have "been holding us here for hours."
"The reason behind it is just, of course, my political views," Kanter, who turned 25 Saturday, said in the video. "And the guy who did it is Recep Tayyip Erdogan, the president of Turkey."
The Thunder said they are working with the league office and gathering information through the appropriate channels.
The players' union is "in conversations with the State Department as well as the league" regarding Kanter, said National Basketball Players Association executive director Michele Roberts, according to the Sports Business Journal. Roberts was speaking Saturday at the Sports Lawyers Association annual conference.
Kanter has been an outspoken critic of Erdogan, which has caused tensions in his home country, as he is one of the most famous professional athletes from Turkey. Kanter is a known supporter of Fethullah Gulen, an Islamic leader and the face of the "Gulen Movement."
During a visit to the White House last week, Erdogan was again caught in controversy as some of his security detail fought with protesters.
"He's attacked people in Washington. He's a bad, bad man," Kanter said in the video. "He is a dictator, and he's the Hitler of our century.
"I will keep you posted guys, but just pray for us, and I'll tell you guys what's going on."
After a letter published by his father last summer in a Turkish newspaper, Kanter announced he had been disowned by his family because of his political views.
"Today I lost my mother, father, brothers and sisters, my family and all my relatives," Enes Kanter wrote in the statement, which was translated to English. "My own father asked me to change my surname. My mother, who has given me life, disowned me. My brothers and sisters, with which we have grown together, ignore me."
In 2016, Kanter, after being outspoken against Erdogan's government following a terrorist bombing in Turkey's capital of Ankara two months earlier, said he received death threats after a failed military coup to overthrow Erdogan.
In June 2015, Kanter said he was left off of Turkey's national team for Eurobasket 2015 because of his politics. National team coach Ergin Ataman said at the time that the decision was not political.
According to Kanter's website, the Light Foundation fosters awareness and provides assistance for children's development through "education, poverty alleviation and social harmony."