The ruling BJP MLA Krishnendu Paul was among those who tested positive on Monday, an official said.
Meanwhile, 161 patients were discharged from various hospitals in the state on Monday, taking the total number of recoveries to 3,565, the minister said.
Of the total 5,853 positive cases, 2,276 are active, nine people have died, 3,565 have recovered and three migrated out of the state, he said.
Paul, the ruling party MLA from Patharkandi in Karimganj district, was tested during the ongoing Assam Targetted Surveillance Programme (ATSP) on Sunday and his report came as positive on Monday evening, the district's Joint Director of Health A Dattari said.
The MLA, who has no recent travel history, has been admitted to Karimganj Civil Hospital's COVID ward, he said.
His home has been declared a containment zone by the district administration and all his family members have been quarantined and their samples taken for testing, the official said.
The Health minister, in a press conference in the evening, said total lockdown may be imposed in Guwahati city as the situation has turned 'alarming' with 144 COVID-19 positive cases without travel history detected in the last two days.
The Kamrup (Metro) district administration, under which Guwahati city falls, has been directed to take a decision to impose total lockdown, when necessary, apart from declaring containment zones in areas from where COVID-19 positive cases have been reported, the minister said.
The lockdown can initially be for a period of seven days and then if necessary, extended for another seven days, he said.
"The situation in Guwahati is alarming and our focus is now on how to control COVID-19 here so that it does not spread to the community level in other districts", the minister said.
He said 181 cases were detected in the city during the last two days and out of these 37 of them had travel history while the remaining 144 patients were from the community without any travel history.
Besides, 114 positive cases were reported from the 12 screening centres in the city where people had gone voluntarily to get their samples tested, he said.
"If this spike continues, we will get 200 to 300 cases daily from Guwahati alone whereas we are getting around this number from across the state now", he said.
Positive cases have been reported from across the city but one common factor that the patients have is a connection with the city's commercial hub Fancy Bazaar, the minister said.
In a bid to tackle the situation, besides the Guwahati Medical College and Hospital (GMCH) and Mahendra Mohan Choudhury Hospital (MMCH), 31 screening centres will be set up in each ward of the city where people can give their samples for testing from Wednesday.
These screening centres will be gradually converted into make-shift hospitals, Sarma said.
The last of the special and Shramik trains were scheduled to arrive by June 23 and "we expect the pressure on quarantine facilities to come down by the first week of July", he said.
"We, therefore, plan to convert the institutional quarantine facilities in Guwahati to COVID care hospitals where asymptomatic patients will be kept for treatment", he added.
He appealed to the people to cooperate by wearing masks and maintaining social distancing "so that it does not turn like Mumbai, Delhi or other places with high positive cases in the next seven or ten days".
"If people cooperate, we can contain it (virus infections)," the minister said.
Assam recorded the highest single-day spike of 331 cases on Sunday, but "there is no need to panic on that account as the number of testing samples has increased", Sarma said.
"I take pride in sharing a big accomplishment of my team in health department and NHM as Assam has reached a record three lakh testing. Our testing count stands at 3,01,557 on June 22", he said.
The minister said that so far 2,43,414 people have entered the state by road, trains and air and "all have been tested and quarantined". DG AD