His plan to boost infrastructure investment was welcomed by the British Chambers of Commerce and the Royal Institution of Chartered Surveyors.
Meanwhile, the Institute of Directors said his intention to renationalise the railways and to raise business taxes would undermine the UK economy.
It said business would "make its case".
The most positive response came from RICS.
Jeremy Blackburn, the organisation's head of policy said: "He has raised some challenging but principled issues around the expansion of Right to Buy to private landlords; as well as providing a voice for the widely-felt dissatisfaction of privatisation in our rail sector. There is undoubtedly opportunity in his agenda around infrastructure and public spending to get Britain building, and we look forward to sitting round the table and discussing this further. "
John Longworth, director general of the BCC, also highlighted Mr Corbyn's infrastructure plans: "Firms will be encouraged by recent statements favouring much-needed investment in the UK's inadequate infrastructure and skills.
"We will be looking for the opposition to take a pragmatic and practical approach to business recognising that wealth creation is the necessary prerequisite for the delivery of any political objectives."
But there was a warning from Simon Walker, director general at the IoD: "From renationalising the railways, to raising taxes on businesses and increasing government spending, Corbyn has proposed some policies in the leadership campaign that we believe would undermine our open and competitive economy."
Mr Walker added that business leaders were never in "perfect agreement" with politicians of whichever party, but that the IoD would give its views "sincerely" in discussions on matters such as state investment in infrastructure and excessive pay at big companies.
Jeremy Corbyn's election as Labour leader has received a mixed reaction from business, including a cautious welcome for his plan on infrastructure.