The playing surface was made tricky by a series of heavy downpours that played havoc with the passing game of both sides, meaning chances were at a premium.
Nick Proschwitz tried his luck from distance early on for the visitors but Ben Hamer was equal to the challenge.
The hosts' first chance fell the way of Bradley Pritchard, who latched on to Yann Kermorgant's flick-on but saw his shot smartly blocked by Alex Bruce.
With 15 minutes gone Johnnie Jackson headed tamely at Ben Amos when well placed and moments later Bradley Wright-Phillips drilled a left-footed shot into the goalkeeper's midriff.
There was a brief moment of panic for the Addicks when City had strong appeals for a penalty waved away following Leon Cort's challenge on Corry Evans.
And their hearts were in their mouths once more on the half-hour mark as Sone Aluko raced through on goal but blasted his strike straight at Hamer.
Thunder and lightning made an appearance shortly before the interval and the hosts could have ended the half with a bang but Cort headed Jackson's inswinging corner just wide.
Both sides struggled to retain possession in the second half as the conditions became increasingly difficult, with numerous misplaced passes disrupting the flow of the game.
Dale Stephens saw a late free-kick deflected wide, with former Leicester defender Michael Morrison inches away from making contact.
But it was the Tigers who finished on top and Aluko's powerful strike was well blocked by Cort before Danny Hollands threw himself in front of Paul McKenna's follow-up.
There was still time for Hamer to perform heroics as he first blocked substitute Jay Simpson's effort before picking himself up to deny the onrushing Aluko when he looked certain to score.
The draw maintains Charlton's unbeaten start to the league season, while Hull have now kept two clean sheets in their opening three matches.