The Clydesdale Bank Premier League meeting at Tannadice takes place on the same day as Scotland's RBS 6 Nations clash with Ireland and will start just 30 minutes after the Capital One Cup final gets underway at Wembley.
All three matches will be screened live for television but Fenlon insists the SPL risk alienating travelling supporters by asking them to attend matches scheduled so thoughtlessly.
He said: "We have played every day of the week since I've been here and almost every possible kick-off time too. It's difficult for supporters to even plan what games they will go to.
"I don't know what it's about - it's madness.
"Our supporters have been asked to travel the length and breadth of the country on different days and at different times. It's difficult to keep asking people to do that.
"And what you do is make people become fed up with that end of it and they turn away.
"You also look at the other attractions that are on this Sunday. There's a big rugby game on and the League Cup final in England. It's very difficult to get people in no matter what, then you go and throw in a ludicrous kick-off time and that doesn't help.
"It's time that people started to look at one of the core aspects of football - the supporters - and ask them what they want. We can't accommodate everyone but they are the ones who make football matches, so they should be included more."