The delivery company hopes to be valued at up to £8.8bn when it lists its shares in April.
But Aberdeen Standard and Aviva Investors, which manage over £800bn combined, said they were put off by the working conditions of its riders.
Deliveroo responded by saying riders had “freedom” to choose their hours.
Deliveroo riders are self-employed, meaning they are not entitled to earn a minimum wage from the company, or holiday and sick pay.
Andrew Millington, head of UK Equities at Aberdeen Standard, told the BBC’s Today programme that the conditions were a “red flag”, adding: “We wouldn’t be comfortable that the way in which its workforce is employed is sustainable.”
He went on to compare Aberdeen Standard’s recent decision to sell off Boohoo shares, following allegations of worker exploitation at the online clothing company.
Large institutional investors such as Aberdeen Standard manage money on behalf of organisations, including pension funds. When they invest in a company, they can try to influence the way it is run – such as through relationships with managers and shareholder votes.
But Mr Millington said that sometimes “disinvesting or not investing in the first place is our only option”.
He added that it would be interesting to see whether Deliveroo can attract investors over the longer term “without making progress” on worker rights.
David Cumming, chief investment officer at Aviva, told the Today programme investors were taking social responsibilities “a lot more seriously”.
“A lot of employers could make a massive difference to workers’ lives if they guaranteed working hours or a living wage, and how companies behave is becoming more important.”
He pointed out that Deliveroo workers are “currently classed as riders [which means] they don’t necessarily get basic rights for minimum wage, sick leave or holidays”.
“We won’t be investing in Deliveroo for a number of reasons but that is one of them,” he said.
Mr Cumming also warned of the risk that drivers will have to be reclassified as workers, which would entitle them to rights such as sick and holiday pay.
“It’s an investment risk if the legislation changes,” said Mr Cumming.
Uber recently chose to reclassify its drivers as workers after a landmark UK supreme court case last month.
Since losing a five-year legal battle with drivers who claimed it had wrongly classified their employment status, Uber has offered holiday pay, a guaranteed minimum wage, and pensions benefits to its drivers.
Other gig economy companies have been looking closely at the Supreme Court’s verdict in February, although it does not directly apply to Uber Eats – the food delivery arm of the business.
Deliveroo has set aside more than £112m to cover potential legal costs relating to the employment status of its delivery riders.
It warned potential investors of the risk of litigation around the world in documents setting out its plans for a stock market debut published on Monday.
“The European Commission is set to draw up new legislation governing how the gig economy model works across the bloc,” pointed out Susannah Streeter, an analyst at Hargreaves Lansdown.
“If Deliveroo is forced to change the way it classifies its riders in the future, it is likely to puncture its profits prospects, and could even derail the delivery giant.”
Mr Cumming said there was a “combination of investment risk and social issues that affect our judgment whether the shares are a buy or not”.
Deliveroo, which was founded in 2013, has said it will hand its riders bonuses of between £200 and £10,000 when it floats, depending on the number of orders they have delivered.
A spokesman said: “We are proud to provide work for 50,000 riders in the UK and that thousands more people apply to work with us every week.
“There has been a strong investor interest in our planned IPO and we are already backed by some of the most respected global tech investors.
“Deliveroo riders are self-employed because this gives them the freedom to choose when and where to work.
“We are confident in our business model, which has been upheld by UK courts three times, including the High Court twice.”