The Scottish Premier League meeting against Dundee United 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."
On Friday, Fenlon confirmed financial restrictions mean he will not be making a move for former Easter Road favourite Kevin Thomson, despite offering him training facilities.
However, with the battle for the top six and European places still so fierce, he admits he still cannot even begin to think about summer targets he can afford.
He said: "I wish I could start looking ahead to next season. I wish I was in the position to do that.
"We still have so much to play for and we need to make sure we get into that top six, which is a real priority for us, and we have a semi-final of the cup at stake too. So we have all that to worry about before we can start to think about next season."
United came out on top in Hibs' last visit to Tannadice with a 3-0 win, but with just 11 points separating Motherwell in second place from St Mirren one up from the bottom, Leith manager Fenlon knows a much better performance is required this time round.
He said: "They are all huge games for us right now. There is something at stake in all the games, which is unusual at this stage of the season as the Old Firm are usually miles ahead.
"But there is a lot at stake right now and that is good for the punters and everybody else."