Approximately 21,000 healthcare workers and first responders have been vaccinated since the rollout last week, the governor said Tuesday.
The state health department said they're moving quickly, allowing phase two to begin soon.
The state began vaccinating nursing home residents and staff members against COVID-19 on Tuesday.
Frances Wantland, 89, was first in line.
CVS and Walgreens are helping the process move quickly. The companies are sending pharmacists and staff to senior and long-term facilities.
"We've deployed over 60,000 pharmacists across the United States across nursing homes, and we will deliver the initial vaccine within three weeks," said Shea Hudson, the regional director for CVS Health.
Staff and residents at all long-term care facilities are part of the first phase of the state's vaccination plan, while the state health commissioner said they are ready to move ahead to phase two.
"Actually, we've had really good uptake. We are just moving quickly through our plan," said interim state Commissioner of Health Dr. Lance Frye.
"Just because we talk about moving on to phase two does not mean we are completely done with phase one. We have overlap, and we need to do that for efficiency's sake," said Keith Reed, the state deputy commissioner of health.
The state expects to receive another 50,000 doses of the Moderna vaccine on Tuesday.
"It will take about 30 days before the date they received their initial dose to have the 95% of immunization that we need from it," Frye said.