A statement on Sunday from the FBI's Seattle office said the bureau remains "committed to investigating crimes that are potentially hate-motivated", The Seattle Times reported.
The 39-year-old victim, a US national of Indian origin, was identified by External Affairs Minister Sushma Swaraj as Deep Rai.
"I am sorry to know about the attack on Deep Rai, a US national of Indian-origin. I have spoken to Sardar Harpal Singh, the father of the victim," Sushma Swaraj tweeted.
"He told me that his son had a bullet injury on his arm. He is out of danger and is recovering in a private hospital," she said.
Rai was working on his car in front of his house in Kent city on Friday night when the gunman, described as white and who had his face partially covered, opened fire at him and fled, the police said.
"This is a top priority investigation, and we are doing everything possible to identify and arrest the suspect," Kent Police Chief Ken Thomas said, adding that the city of about 120,000 should "be vigilant".
Thomas said the victim has been released from the hospital.
The shooting also created fear within the Sikh community with its members calling on law enforcement to investigate the racially-motivated attack, the Seattle Times reported.
Jaswinder Singh, of the Gurdwara Sikh Center of Seattle, said the group has received many calls and messages of support since the incident.
"It's kind of scary to hear about things like this, but we definitely have been getting tremendous support from the community," he said.
The Sikh Coalition, a national civil-rights group, asked local and federal authorities to investigate the shooting in suburban Seattle as a hate crime.
The attack reverberated across the nation, with Mayor de Blasio condemning it from New York.
"As mayor of the city with the nation's largest Indian community, my message is clear: this is your city and this is your country," De Blasio tweeted.
Sikh community leader in Washington state, Satwinder Kaur, said: "Everybody who is part of this community needs to be vigilant."
"It is scary. The community has been shaken up," he said.
The incident comes after 51-year-old Adam Purinton fatally shot Srinivas Kuchibhotla, an aviation engineer, and wounded Alok Madasani, both Indian and 32, at a Kansas City bar last month.
Purinton was charged with premeditated murder and two counts of attempted murder.
Authorities are investigating the attack as a hate crime after witnesses said he was drinking hard and started yelling racial slurs, including "get out of my country".