The FMA is concerned that investors are being coaxed with big returns without the context of the atypical period.
The FMA notes shifting the performance period back just one month makes a significant difference to the results.
The NZX50, for instance, shifts from a gain of 23.94 per cent to the more moderate 7.7 per cent.
These shifts are also seen across the MSCI World fund and the S&P 500.
The FMA said it had engaged with industry bodies on this issue.
"Encouragingly, some fund managers with growth products share our concerns and have already told us they will not be promoting performance focused exclusively over this 12-month period," said FMA director of investment management Paul Gregory.
The FMA has asked KiwiSaver providers, fund managers and financial advisers to avoid advertising performance for the 12-month period to March 31, 2021.
It has further asked fund managers to ensure the content or tone of their advertising does not place undue emphasis on performance over the 12-month period.
"Where a provider decides to, or continues to, promote the strong returns seen over the 12 months to March 31, we will be closely monitoring whether doing so potentially breaches the fair dealing provisions contained in the Financial Markets Conduct Act 2013," Gregory said.
"We will also be concerned for the interests of any members who joined the provider's scheme or switched into higher-risk funds during the promotion period."
The FMA is currently looking at firming up the advertising rules, taking particular aim at the habit of fund managers to cherry-pick information to create a more favourable impression.