South Africa claimed a rain-reduced five-over contest by 14 runs in the opening game in Cardiff on Wednesday, before England registered a record 146-run win in the second fixture in Manchester on Friday as Phil Salt scored an unbeaten 141.
That result set up a grand finale on Sunday, but persistent rain in Nottingham delayed the toss and ultimately meant no play was possible.
"It's a shame that the weather has ruined it again," England captain Harry Brook said.
"We only played one T20 game, but the way that we played the other night was phenomenal. For us to do that against a very strong side gives us a lot of confidence."
South Africa won the One Day International series between the sides 2-1.
England now move on to a three-match T20 series against Ireland that starts in Dublin on Wednesday.
"We had a lot of motivation today to put in a good performance and rectify a few things, but it is frustrating with the weather," Proteas skipper Aiden Markram said.
"We're tracking towards that World Cup … the other night was a tough performance, we were completely outplayed. Today was an exciting opportunity, a must-win game. It's as close as you can get to a World Cup. But when the weather is like this, there's not much you can do."
