Danciulescu, who made his league debut exactly 19 years ago for Electroputere Craiova, also played for Dinamo's bitter city rivals Steaua between 1998-2001.
"Records? I don't really care about them," he told local media. "I just want to play well and help my team achieve good results."
Danciulescu, who turns 36 in December, broke the previous record of 490 appearances set by former Steaua Bucharest and Universitatea Craiova defender Costica Stefanescu between 1969-88.
The striker is also the second highest scorer in the league with 210 goals, 148 for Dinamo, behind Dudu Georgescu (252).
Danciulescu has won eight caps for Romania. His most memorable performance came when he scored twice in a 5-1 win over Germany in a friendly in 2004.
Dinamo are fifth in the table with 18 points from 10 games, seven points behind leaders Steaua.