Mr Ritter tragically died from a brain tumour last month aged 54.
Ms Greig, also 54, opened an anniversary special of the hit show with a special message about her co-star.
She described Mr Ritter, who played her on-screen husband, as a “true friend”.
She said: “I'm sure you know that very recently we lost our dear and most cherished friend Paul Ritter, who plays Martin Goodman in Friday Night Dinner.
“We all miss him terribly, incredible actor, a true friend and a lovely human being. Sadly at the time of making the documentary, Paul was pretty unwell and to be honest - don't tell the producers - I did try and persuade him not to do the interview.
“But it is testament to Paul's courage and generosity and dignity and complete lack of vanity that he wanted to participate in the documentary, do an interview and to really celebrate this little world that he's been a part of and that he's enjoyed so much over the years.
“So I know that Paul would want us to all sit back and laugh and enjoy this celebration of the FND universe. And say, as we do, in his memory - shalom.”
The show’s fans took to social media to share that the tribute had left them “sobbing” and “in tears”.
One fan wrote: “Cheers Tamsin, I'm in tears already #FridayNightDinner”, while another said: “Sobbing already #FridayNightDinner.”
A third added: “Already getting choked up. #FridayNightDinner,' and a fourth person asked: 'Anyone else already crying? #FridayNightDinner.”
Someone else tweeted: “Makes me emotional to know that they'll never work together again #FridayNightDinner.”
The Channel 4 sitcom, which first aired in 2011, centred around a middle-class Jewish family who met for a weekly meal at their home in north London.
The anniversary special, entitled Friday Night Dinner: 10 Years And a Lovely Bit of Squirrel, looked the show’s funniest moments.
Mr Ritter’s character Martin Goodman was well-known for his catchphrases which included “s**t on it” and “that's a lovely bit of squirrel”.
The actor died at home last month with his wife Polly and sons Frank and Noah at his bedside.
Last month, a spokesman for the actor announced his passing and said: “It is with great sadness we can confirm that Paul Ritter passed away on Monday night.
“He died peacefully at home with his wife Polly and sons Frank and Noah by his side. He was 54 and had been suffering from a brain tumour.
“Paul was an exceptionally talented actor playing an enormous variety of roles on stage and screen with extraordinary skill. He was fiercely intelligent, kind and very funny. We will miss him greatly.”