The unrest began early in the match on Saturday with the repeated use of pyrotechnics in both home and away supporter sections, a police statement said.
Fans entered the field, prompting police to intervene, separate the groups, and secure the area. The match resumed after a 20-minute interruption.
"As part of the operation, the Dresden police initiated more than a dozen investigations for breach of the peace, dangerous bodily harm, property damage, insult and ticket fraud," the statement said.
Dynamo Dresden expressed deep regret over the scenes at the Rudolf Harbig Stadion, with finance director Stephan Zimmermann apologising to uninvolved spectators.
"Our home games are known for their unique atmosphere. Images like those we saw tonight are unacceptable and massively damage not only our club, but football as a whole in Germany," he said in a statement on Sunday.
Hertha Berlin won the match 1-0 after an 80th-minute goal by Marten Winkler, leaving the capital side in sixth place in the Bundesliga 2 standings while Dresden are 15th.