Griner was escorted out of the courtroom in handcuffs by police after the ruling, turning to reporters and saying: "I love my family".
Griner, a two-time Olympic gold medallist and Women's National Basketball Association (WNBA) star, was arrested in mid-February as she arrived to play for a Russian side during the WNBA offseason. Her case threw the Texan into the geopolitical maelstrom triggered when President Vladimir Putin sent troops into Ukraine on Feb. 24, propelling U.S.-Russian relations to a new post-Cold War low.
Her sentencing could now pave the way for a U.S.-Russia prisoner swap that would include the 31-year-old athlete and an imprisoned Russian who was once a prolific arms dealer.
Griner had admitted having the vape cartridges containing hashish oil but said she had made an honest mistake by inadvertently packing them.
Before the verdict, she tearfully pleaded with a Russian judge not to "end her life" with a harsh prison sentence. The court also fined her 1 million roubles ($16,990).
Biden, under pressure to bring home Americans held in Russia, called on Russia to free Griner immediately and said his administration would continue to work for her release.
"Today, American citizen Brittney Griner received a prison sentence that is one more reminder of what the world already knew: Russia is wrongfully detaining Brittney," he said in a statement.
"It's unacceptable, and I call on Russia to release her immediately so she can be with her wife, loved ones, friends, and teammates."
National security spokesperson John Kirby later on Thursday urged Russia to accept a "serious proposal" Washington made weeks ago for Griner's release.
Griner's lawyers said they would appeal a verdict they said was "absolutely unreasonable". Her defence team said the court had ignored all evidence they had presented, as well as Griner's guilty plea.
"She is very upset, very stressed," said Maria Blagovolina, partner at Rybalkin Gortsunyan Dyakin and Partners, after the hearing. "She can hardly talk. It's a difficult time for her."
The Russian prosecutor had called for Griner to be sentenced to 9-1/2 years prison if she was found guilty of bringing illegal drugs into the country.
Griner was detained at Moscow's Sheremetyevo airport on Feb. 17 with the cartridges containing hashish oil in her luggage. While she pleaded guilty, she said she had neither intended to bring a banned substance to Russia nor to hurt anybody.
"I made an honest mistake and I hope that in your ruling, that it doesn't end my life here," Griner said in court on Thursday before breaking down in tears.
"My parents taught me two important things: one, take ownership of your responsibilities and two, work hard for everything that you have. That's why I pled guilty to my charges."
"I want to say again that I had no intent on breaking any Russians laws," she told the court. "I had no intent, I did not conspire or plan to commit this crime."
Griner also referred to the international politics around her case, saying: "I know everybody keeps talking about political pawn and politics, but I hope that is far from this courtroom".
Cannabis is illegal in Russia for both medicinal and recreational purposes.
Griner's defence team had called for her to be acquitted. Alexander Boikov, one of her lawyers, said some of the case files had been drawn up in violation of the law.
The United States has offered to exchange Russian prisoners for American citizens including Griner and former Marine Paul Whelan.
One source familiar with the situation said Washington was willing to exchange convicted arms trafficker Viktor Bout, whose life helped inspire the 2005 Hollywood film "Lord of War" starring Nicholas Cage.
Russian officials have said a deal has not been reached. They argue that Griner - known as "BG" to basketball fans - violated laws and should be judged accordingly.
USA Basketball said in a message on Twitter it was disappointed at Thursday's ruling but it would remain engaged with the U.S. State Department in the effort to get Griner home.
"We will not be satisfied until BG is back in the U.S. and reunited with her loved ones, teammates and fans," it said.
WNBA Commissioner Cathy Engelbert and NBA Commissioner Adam Silver said in a statement that the verdict against Griner was "unjustified and unfortunate."
Griner appeared at the hearing in a grey T-shirt and round-rimmed glasses. Before taking a seat in the defendant's cage, she held up a picture of UMMC Ekaterinburg, the team she played for in Russia during the WNBA offseason.
In her testimony last week, Griner expressed puzzlement as to how the vape cartridges ended up in her luggage as she was flying to Russia to join UMMC Ekaterinburg for the playoffs.
Teammates and friends urged the Biden administration and Putin's government to negotiate her release.
"I hope that, now that the sentencing has occurred, the trial is over, no more court, that the negotiations will proceed," her high school basketball coach Debbie Jackson told Reuters.
"I’m praying that both sides will negotiate in good faith and that Brittney and other Americans that are in Russian prison can come back home."
($1 = 58.8500 roubles)