Of them, 586 were added on Sunday, according to the Public Health Emergency Operations Center.
People are suspected to be infected when they have symptoms like cough, fever and shortness of breath and have come from outbreak areas or have had direct contact with returnees from stricken areas.
Those tagged as suspect are quarantined in hospitals meant for Covid-19 treatment and tested twice for the virus.
In January the highest number of suspected cases a day had been 97, and in February it had been 304.
Besides quarantining, Vietnam has also placed many others under medical monitoring - those coming from virus-hit areas or into contact with infected people but not showing any Covid-19 symptoms.
They are routinely checked at ports of entry before being sent to medical camps for 14 days of monitoring. Some people with low risk of infection are quarantined at home and checked by local medical personnel every day.
Anyone with Covid-19 symptoms like cough or fever are then quarantined in hospitals. If they test negative for the coronavirus, they will undergo additional monitoring at home or a medical camp.
As of Monday morning there were more than 52,700 people placed under medical monitoring, also the highest number in three months. Over 30,000 of them are isolated at home.
As of Sunday Vietnam had 113 confirmed cases, with 19 added on Sunday alone.
They include 96 still in hospital while the remaining 17 recovered and were discharged from hospital.
Covid-19 has spread to 192 countries and territories, killing more than 14,600 people so far.