Underwood suffered a head injury and Hearn hurt his ankle last weekend in Glasgow, where the Canadian men tied for seventh.
"It's a blow to us because obviously they were very influential players in the last two tournaments," Canadian coach Liam Middleton said Friday from London.
Middleton has called in Connor Braid (Glasgow Warriors) and Matt Evans (Cornish Pirates).
Canada hopes to reach the Cup quarter-finals for the third event in a row as the nine-event HSBC Sevens World Series wraps up its season in London.
Prior to Glasgow, the Canadian men finished fourth in Tokyo.
"I think we've just started to get things together a little bit more," said Middleton, a Zimbabwe native who missed the first stop of the season due to immigration red tape after being named coach in September.
"It takes time for a new coach to come in and implement new ideas and a new culture within the team."
Middleton has also had to battle injuries and juggle splitting his squad with the 15-man national team.
"It was quite difficult to get going but I certainly feel with Tokyo and Glasgow we're starting to see a lot of things we do on the pitch coming through," he said. "It's now just really about trying to grow at each tournament but also trying to find a little bit of consistency."
Canada, which currently stands 11th in the overall standings, has been drawn in a tough pool with series leader Fiji, No. 8 Argentina and No. 9 Samoa. The Canadians lost 21-12 to Argentina last weekend.
The top two will advance to the Cup quarter-finals.
The two four teams in the overall standings at the end of the weekend automatically qualify for the 2016 Olympics. Fiji, No. 2 South Africa and No. 3 New Zealand have already booked their ticket with No. 4 England likely to join them barring a total collapse.
Canada will look to a regional qualifier in June when they will likely have to beat the U.S. to qualify for Rio de Janeiro. The loser will get one last chance via a world repechage.
The Canadian men finished sixth in the 2103-14 World Series standings.
Calling this a transitional year, Middleton said Olympic qualification remains the big prize.
"It doesn't matter where we finish up this weekend as long as we're performing well and making improvements in our game."
Day 1 of the London event has been sold out, meaning a crowd of 75,000 will be in attendance at Twickenham Stadium.
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