Alison Evison, the president of council umbrella body Cosla, said one newly elected councillor had told her she required three different babysitters due to her working hours.
Ms Evison suggested the length and timing of council meetings could be adjusted to boost diversity and encourage more people to stand for election.
Councillors receive a basic annual pay of £19,571 in Scotland. Cosla has pushed for them to be paid at least the real living wage of £9.90 an hour.
A survey in June 2021 found financial barriers were cited by several female councillors who were either stepping down or considering it.
Women also highlighted the challenges of balancing caring responsibilities with the role.
Cosla and the Scottish Government previously committed to an independent review of councillor pay "as soon as possible" after the local elections. This is expected to begin work in the autumn.
Ms Evison told The Scotsman: "I think many people in our communities think that councillors are paid like members of Parliament and that is certainly not the case, by any means."
She said the low rate of pay was "certainly" putting diverse candidates off standing for election, adding: "A lot of women in particular are finding they can't stand for a second term of office because they literally cannot afford to have their family cared for while they're doing that work.
"So it is putting people off and it's obviously not helping the diversity as well, when you see experienced people from already underrepresented groups feeling they have to step down from standing for a second term of office."
Ms Evison said she recently met a new councillor "who was talking about having to find her third babysitter" because of her working hours.
She said councils' standing orders – the rules that govern how they operate – "were set by a particular demographic to suit their particular needs".
Ms Evison added: "They can be altered through democratic processes, and that is crucial – that we have systems in our councils, in this case, that are appropriate to the people currently serving in them.
"We can't let people be put off standing because the systems in place now aren't right for the life I lead and my caring responsibilities and everything else.
"They can be adjusted and we need to be more willing to make the adjustments necessary to encourage more people to stand for elected office.
"It's really crucial if local democracy is going to be meaningful across Scotland."
Ms Evison said the length and timings of meetings could be "a good place to start".
Elsewhere, she said action needs to be taken to improve civility in public life and tackle social media abuse.
A Scottish Government spokesman said: "It is important that we encourage a wider range of people to seek election, including more women, ethnic minorities and younger people, so that councils can better reflect the society we live in.
“The Scottish Government and Cosla have committed to an independent review of councillor pay and we are working at pace following the recent local elections to ensure that terms and conditions truly reflect the responsibilities of the 21st-century councillor.”