... the England international scored for a record-equalling 10th game in a row.
Vardy moved alongside former Manchester United striker Ruud van Nistelrooy, who managed to find the net in 10 successive Barclays Premier League fixtures in 2003, by firing home in first-half stoppage-time in a 3-0 success over Newcastle.
Leonardo Ulloa and substitute Shinji Okazaki were also on target but it was Vardy's individual feat that garnered the most attention.
"I'm very, very happy for his performance," Ranieri said.
"It's not easy to equalise a big champion. I want to say, 'Well done and thank you!'
"When a manager has a striker who is scoring goals, he's very happy. I want to say it's a great achievement - I hope he can beat it next match."
Vardy will have the chance to eclipse Van Nistelrooy's achievement when Leicester face his old club United in seven days' time in the midlands.
The Dutchman had posted a message on Instagram on Friday encouraging Vardy in his pursuit of the record, a fact the England international was made aware of prior to kick-off.
And the universal admiration for Vardy was evident at St James' Park too as Newcastle fans applauded him off at the interval and when he was substituted with 13 minutes remaining.
Ranieri praised the Newcastle fans for their appreciation of Vardy and likened it to the response opposing fans used to give likeable Chelsea forward Gianfranco Zola.
"It's fantastic, I love the English spirit," Ranieri added. "It's not important, the shirt, it's how the players play. That was the same when I managed Zola. I want to also say thank you to all the fans who clapped Jamie."
Vardy helped Leicester win for the fourth time in five games to keep them in the table's upper reaches.
However, their Italian boss would rather focus on the fact it took them to 28 points, 12 shy of the 40-point mark teams bid to reach to ensure survival.
"I say every time I want to see the horses at the end of the race, now it's not important," Ranieri stressed.
"It's important for us because it's important we have 28 points, 12 (more) and we achieve our goal. After, we can speak about other things but now we are very, very focused on our goal."