Baldock passed away on Wednesday at the age of 31 at his home in Athens. He had moved there in the summer after departing from Bramall Lane to join Panathinaikos.
His family said in a statement on Thursday that he drowned while swimming in his pool.
Most of Baldock's seven years with the Blades came under the leadership of Wilder, who rejoined the club last December.
Speaking in a video on Sheffield United's X feed, Wilder said: "I'm just stunned really.
"I'm quite matter of fact, I think we're getting to that age where we're going to more and more funerals. Obviously through your life you lose people that you love and you respect, but this just feels completely different to everybody.
"Everybody's just absolutely stunned and numb really. It's just tragic."
Baldock, known as 'Starman' to fans, helped United to promotion to the Premier League in 2019 and was a key figure in their successful first season in the top flight.
"He wasn't one to grab the headlines," said Wilder. "But George was a huge personality, a huge driver, a huge culture carrier. George epitomised everything on the pitch and off the pitch.
"He was a humble person. We had rows, we had bust-ups, but we were all driving it forward and after the same outcome in everything that we did.
"Just even thinking about it now, families have lost a son, players have lost a brother. Those boys that went to battle with George, and he stood up to every challenge.
"He was an absolute pleasure to manage. He gave his maximum in everything he did and that's what every Sheffield United fan wants."
Blades owner Prince Abdullah and chairman Yusuf Giansiracusa paid tribute to Baldock on Friday morning.
"Like all Blades, we received the news of George Baldock's tragic and premature passing with overwhelming sadness," a statement read.
"Our thoughts and prayers are with his family, as well as his friends and all who knew him, not least the Sheffield United family.
"George played every minute on the pitch with passion, commitment and the ability associated with our football club, and his role in our campaigns to achieve two promotions will live long in our memories and the history of the club.
"George served United with distinction - he remains a Blade."
Buckingham-born Baldock progressed through the academy at MK Dons before joining United in 2017, and they also paid tribute to their former player.
Dons head coach Scott Lindsey said in a video posted on social media: "All our thoughts go to his family. It's really, really sad news.
"I had the pleasure of coaching George myself. He came to Tamworth on loan from MK Dons and I was the assistant manager at the time and you could see he was going to have a really bright future in the game.
"And, of course, he did. He went on to play at the top level and was outstanding throughout his career.
"It's really sad news. All our thoughts from the football club go to his family and friends."