Machchhar was attacked by another pilot onboard a Flydubai flight bound for Tel Aviv, forcing the plane to divert to Saudi Arabia.
The captain, who has been hailed as a "true hero" by Israeli Prime Minister Benjamin Netanyahu, was taken to a hospital in Tabuk, a city in north-western Saudi Arabia.
The Indian embassy in the United Arab Emirates said Machchhar was "in good health and recovering well". Ambassador Deepak Mittal said he was "proud of Capt Smit for his bravery" and "very reassured" to meet him.
Netanyahu wrote on X that Machchhar "saved the lives of 174 people" and prevented "a catastrophic mid-air disaster".
Machchhar grew up in the Indian city of Mumbai, where his parents still live. In 2008, he joined Mainland Air, an aviation college in New Zealand's Dunedin, before joining Indian airline SpiceJet as a commercial pilot three years later.
He moved to Dubai and joined Flydubai in 2022 as an experienced pilot.
Philip Kean, the CEO of Mainland Air, told the BBC he remembered Machchhar as a man who would remain calm in a crisis.
"We trained him for forced landing - not this kind of situation, which is very, very rare," Kean said. "It was a long time back but he came across as a good and honest worker."
Machchhar has more than 9,750 hours of flying experience, including more than 6,400 hours as pilot-in-command, according to his LinkedIn profile.
His former employer SpiceJet issued a statement calling Machchhar a "hero" who had saved "countless lives".
An old friend who worked with him at SpiceJet, Capt Dharav Gosalia, described him as outgoing and "very jovial".
