Organisers said the race would start at 10am local time (06:00 UK time).
The International Biathlon Union, however, said in a statement: "The postponement was due to fog not only in the stadium but also due to heavy fog on the tracks which created dangerous conditions.
"The new start time will be determined after consultation with the Sochi Organising Committee."
The race was first delayed by one hour from 1900 to 2000 local time but conditions did not improve.
In biathlon, athletes have to complete a distance over skis and stop at a shooting range two or four times depending on the disciplines.
The targets are 50 metres from where athletes stand or lie and were impossible to see on Sunday.
- Sports & Recreation
- International Biathlon Union