Flaco Jiménez, a Grammy-winning singer, songwriter and accordion virtuoso who was widely regarded as the king of Tex-Mex music, recording material that ranged far beyond his roots with acts like Dwight Yoakam, the Rolling Stones and Bob Dylan, has died. He was 86.

His death was announced on Thursday by his family in a Facebook post, which did not say where or when he had died or provide the cause. He had been hospitalized with an unspecified illness and released in January.

The son and grandson of accordionists, Mr. Jiménez played a style often characterized as norteño, Tejano or conjunto — though he preferred the term Tex-Mex because it captured the variety of influences that flowed through his music.

“I would consider our music as like a bouquet of roses in rainbow colors, you know?” he told The Worcester Telegram and Gazette in Massachusetts in 1990. “Just imagine a bouquet of roses with one color. It would be boring, man.”

Mr. Jiménez won six Grammys, five of them on his own and one, in 1999, with Los Super Seven, a rotating collective of Tex-Mex and country artists, including Joe Ely, Freddy Fender and Doug Sahm. In 2015, he won a Grammy Lifetime Achievement Award.

Among his most popular songs are “Ay Te Dejo en San Antonio” (“Ay, I Leave You in San Antonio”), the title track on his Grammy-winning 1987 album; “En el Cielo no Hay Cerveza” (“There’s No Beer in Heaven”); and “El Mojado Sin Licencia” (“The Wetback Without a License”), about the struggles of being an undocumented immigrant.

Mr. Jiménez first made his name around Texas in the 1960s, playing the dirt-floor dance hall scene in cities and towns along the U.S.-Mexico border.

His early style was heavily influenced by the more traditional approach of his father, Santiago Jiménez, who was also nicknamed Flaco, Spanish for “skinny.”

His father, who taught him to play the accordion, had learned the instrument from his own father, who in turn had picked it up from the Bohemian immigrants who settled in the San Antonio area in the early 20th century, bringing along their polkas and waltzes.

But Mr. Jiménez’s sound expanded along with his list of collaborators. In the late 1960s, he played with Mr. Sahm in his band, the Sir Douglas Quintet, which exposed him to rock; in the 1970s, he picked up New Orleans blues from his work with Dr. John, and world-fusion sounds from collaborating with Ry Cooder.

The result was a rollicking, upbeat style that proved enormously influential among younger generations of Tex-Mex musicians. If you’ve heard the jaunty, happy sounds of an accordion-backed quartet recently, then you’ve heard Mr. Jiménez’s legacy in action.

Mr. Jiménez resisted efforts to buttonhole his music as a particular style, or to draw a line between it and other traditions.

“It’s just music,” he told The Los Angeles Times in 1994. “There’s nothing that different about any of it that you can’t find a way for them to meet.”

He was born Leonardo Jiménez on March 11, 1939, in San Antonio. His mother, Luisa (Mena) Jiménez, oversaw the home.

His first instrument was the bajo sexto, a type of 12-string guitar, but he switched to the accordion soon after he started playing alongside his father, when he was just 7.

When he was 15, he formed his own band, Los Caporales. But long after he split with his bandmates, he kept the name as an alter ego of sorts for future lineups, when he wanted to play more traditional music in contrast to the faster-paced, more modern sounds that had come to define him.

In the 1970s, a series of collaborations — with Mr. Sahm and Mr. Cooder, as well as with the documentarian Les Blank, who featured Mr. Jiménez’s family in his 1976 documentary “Chulas Fronteras” — brought Mr. Jiménez to an international audience.

He became a popular session musician. He played alongside Mr. Yoakam and Buck Owens in their 1988 version of “Streets of Bakersfield,” which Mr. Owens had first recorded in 1973 and which brought the trio a gold record.

In 1990, Mr. Jiménez played live alongside Mr. Dylan on “Across the Borderline,” originally recorded by Mr. Cooder, in Montreux, Switzerland. And he played with the Rolling Stones on “Sweethearts Together,” a track on their 1994 album, “Voodoo Lounge.”

Mr. Jiménez also played in a string of influential Tex-Mex bands, including the country-inflected Free Mexican Airforce and the Texas Tornados, alongside Mr. Fender, Mr. Sahm and Augie Meyers.

His survivors include his wife, Adela; their children, Arturo, Gilbert and Cynthia Jiménez and Raquel Fernandez; and his brother, Santiago Jr.

Mr. Jiménez continued to tour internationally long after many of his contemporaries had slowed down, and he maintained vibrant fan bases in Japan and Europe. But he remained a working-class San Antonian at heart.

“Sometimes people say, ‘You recorded with this, you’ve done this, the Grammys and all,’ but actually, I’m not a rich man,” he said on the Robert Rivas radio show in 2015. “I’m just a day-by-day worker, man. My fortune is my kids.”

Víctor Manuel Ramos contributed reporting.