Witnesses told German media the man was intoxicated and shouting criticism of Hollstein's refugee policy, leading authorities to believe the attack was politically motivated.
Mr Hollstein, a father of four and a member of Mrs Merkel's conservative party, appeared shaken as he answered reporters' questions the day after the attack.
The mayor was at a local kebab restaurant around 8 p.m. (1900 GMT) on Monday, when the attacker slashed him on the neck with the knife before restaurant employees overpowered him and called police, Lokalstimme reported. "Thank you also to those who helped him".
"If you ask me whether that knife in his pocket was for me, I'd answer with a yes", he said.
A mayor in western Germany has survived a knife attack amid suspicions of a link to his liberal immigration policy. At a news conference Tuesday, he credited the kebab shop owner, Abdullah Demir, as well as Demir's wife and son, with intervening to save his life. Police later arrested the assailant.
Mr Hollstein was taken to hospital but discharged later on Monday. He said he had a 15 centimetre-long cut on the left side of his neck. The attacker had an "alleged xenophobic motivation". The man allegedly said he attacked Hollstein because the mayor has voluntarily taken in more refugees in Altena than the town is obliged to according to the federal distribution key for asylum seekers.
German authorities have been alarmed by growing violence against refugees and pro-refugee politicians in recent years. The influx saw an outpouring of support from many Germans who wanted to help the refugees, but also a sharp rise in the number of attack against migrants and sometimes also against their supporters.
North Rhine-Westphalia's CDU state premier, Armin Laschet, has described the assault as politically motivated.
The assault revived memories of a knife attack on Cologne's mayor Henriette Reker in October 2015 by a rightwing extremist angered by her liberal position on refugees. She has since made a full recovery.
While most mainstream parties back the principle of Germany taking in people fleeing war zones such as Syria, the backlash led the far-right Alternative for Germany (AfD) party to win its first seats in parliament in September's general election.
"I'm going to continue to work for refugees, for those who are already here and for those who are still arriving, for the weak and the strong in our society, like a good mayor should", he said.