A statement issued by the department said a casualty each was reported from Madhepura and Begusarai districts.
It did not provide details such as age, sex and travel history of the two deceased.
Of the 23 deaths, Khagaria district accounts for three, followed by two each in Patna, Vaishali, Begusarai, Siwan and Bhojpur, and one each in Munger, Rohtas, East Champaran, Sitamarhi, Nalanda, Samastipur, Saran, Bhagalpur, Jehanabad and Madhepura.
The districts leading the chart in terms of COVID-19 cases are Patna (252), Begusarai (245), Rohtas (206) and Madhubani (190).
COVID-19 cases have been reported from all 38 districts of the state and in 14 of those, the tally is in three digits. With nine cases, Sheohar has reported the least number of infections so far.
Although the state had reported its first couple of cases in March, more than 3,000 people tested positive in May, the spike attributed mainly to the massive influx of migrants by special trains and other modes of transport.
According to data released by the health department, the number of migrants who have tested positive for the disease since May 3 is 2,743.
Although the migrants testing positive include returnees from 24 states, a majority of them have come back from Maharashtra (677), Delhi (628), Gujarat (405), Haryana (237), Uttar Pradesh (149), Rajasthan (126), West Bengal (107), Telangana (104) and Punjab (81).
Altogether 1,741 COVID-19 patients have recovered in the state so far while the number of samples tested till date is 78,090.
Anupam Kumar, Secretary in the Information and Public Relations Department, told a media briefing that the process of bringing back migrants was "almost complete", a reason why there has been a drop in the number of Shramik Special trains.
Winding up of the quarantine centres at the block level is proposed by June 15, he said.
The official said with most of the lockdown restrictions being relaxed, the state will now keep an eye on observance of social distancing at public places.
Additional Director General of Police (Headquarters) Jitendra Kumar said the people of the state coughed up a staggering Rs 20.42 crore towards fines imposed for violating the lockdown, which ended on Sunday. The number of arrests made was 2,442, while 2,260 FIRs were registered.
As many as 85,345 vehicles were seized during the 67-day period for plying without observing the lockdown guidelines, he added. NAC NN RC