Match officials called off play in the afternoon, without the teams taking to the field at Dhaka's Sher-e-Bangla stadium following continuous heavy showers.
Bangladesh reached 246-8 in their first innings on the opening day, before rain prevented a single ball being bowled on the second, third and fourth days.
South African paceman Dale Steyn took 3-30 on the first day, making him just the 13th cricketer in history to claim more than 400 Test wickets.
"We have been preparing ourselves to get on the park. The field has been unbelievable. We were really surprised how well the drainage works here," he said.
Bangladesh batsman Riyad Mahmudullah said the team was struggling to stay focused.
"When you take preparation both physically and mentally for playing five days and see three days of washout, it becomes very irritating," he said.
