Racing drivers, officials and mechanics assembled ahead of the start of the race in Singapore to remember the life of "Dr Sid".
The renowned British neurosurgeon, who served the sport for 26 years, died of a heart attack, aged 84, earlier this month.
But as the group fell silent, with images of Watkins shown on a large screen, Mercedes driver Schumacher was nowhere to be seen.
The seven-times world champion admitted afterwards he had been caught short ahead of the race and was on the loo for the sombre moment.
"I have to apologize. I was still on the toilet," Der Spiegel magazine reported Schumacher saying.
"My thoughts were with Sid though,” he added.
Several drivers paid tribute to the doctor over the past week, including Schumacher who described him as a friend "with whom I share many memories, both professional and private".
Watkins, who leaves behind a wife and six children, was with Formula 1 from 1978 until 2004 and is credited with saving the lives of many drivers including Gerhard Berger, Mika Hakkinen and Rubens Barrichello.