Poulter brought the matter to light with a series of tweets in which he called Matsuyama an "idiot."
They played together in the third round Saturday, and Matsuyama walked down the practice range when he saw Poulter.
"I heard about it this morning, I felt really bad," Matsuyama said after his round at the Cadillac Championship. "All I can do is apologize for what happened.
"I feel badly that he even had to write about something I had done."
Matsuyama missed a seven-foot par putt in the second round Friday and slammed his putter into the green, leaving what one caddie described as a 1.5 centimetre gash.
Poulter wasn't affected by the damage. The gash in the turf was directly in the line of Charl Schwartzel's 12-foot par putt, and a rules official was called out to repair the damage before Schwartzel could putt. He missed and made bogey.
The incident escaped noticed until Poulter, with over 1.6 million followers, took to Twitter late Friday.
"Playing with Matsuyama tomo. He buried his putter in the 13th green 5 ft from the hole, Referee had to repair the crater. Because he didn't," the first tweet said.
Poulter followed with two more tweets:
— "Why should Matsuyama leave a crater in the green for others to putt over, or have to call a referee to repair the damage. Idiot."
— "Im no saint & first to say. But that was disgusting. I wouldn't bury a putter in a green 5 ft from a hole & have players behind deal with it."
Matsuyama, the No. 22 player in the world who last year became the first rookie to win the Japan Golf Tour money list, walked over to Poulter with his interpreter, Bob Turner. He shook hands with Poulter and apologized.
"I made loads of mistakes," Poulter told him. "If you're going to do it, repair it."
Poulter ended the brief exchange by saying, "No words today," indicating there was no need to bring it up again during their third round.
And apparently they didn't. Matsuyama called it a "normal round." He shot 71, while Poulter had a 73.
"The kid's a good guy, a good golfer," Poulter said after his round. "He's a great golfer.
"We all made mistakes. He said sorry. He didn't have to apologize to me. It's got nothing to do with me. It was in Charl's line, not my line."
Matsuyama sought out Schwartzel and Jason Dufner, who also was in the group, to apologize.
"I felt a responsibility to seek them out and apologize to them directly," Matsuyama said through his interpreter. "They were in the threesome directly behind us.
"It didn't affect my preparation today. I felt like it was something I should do. Hopefully, I learned I need to be more patient. In the future, I'll try my best to be a good professional."