The 41-year-old Zimbabwe-born batsman reached the landmark when he made 49 in Worcestershire's English county championship match against Warwickshire at Edgbaston.
Hick, who made 65 Test appearances, is the first player to make 40,000 runs since Graham Gooch did so 13 years ago.
Despite reaching the landmark, the right-hander, who has an average of 52.56, vowed to keep playing.
"You can look back at things like that and feel proud about realising the achievement - but it is not something you set out to do," said Hick.
"It is a good achievement but hopefully now I've passed it I can carry on.
"It is nice to reach it but there are other important things, us winning, us playing well, which are more important and mean more to me than just getting past a certain total of runs.
"I am not really that fussed about it. I know later on it will be nice to look back and see what you have done, I suppose."
Worcestershire skipper Vikram Solanki praised Hick's achievements.
"I can't speak highly enough of Graeme. To score 40,000 runs is difficult for me to comprehend," said Solanki.
"I remember coming into the dressing room as a young kid and being overawed by the fact Graeme Hick was in the dressing room.
"As a player, he is the ultimate professional. He is still in fine shape. He has always looked after himself, he is still fit, still works hard, probably harder than anyone else now. He is an amazing guy."