She said, rather than resort to name-calling, insults and other scathing attacks, the focus must be on her record.
Prof Opoku-Agyemang was on Monday outdoored as John Mahama’s running mate for the 2020 elections.
To this end, she becomes the first vice-presidential candidate of a major political party in Ghana.
Mrs Owusu-Ekuful said political opponents must desist from attacking the NDC vice-presidential candidate because she’s a woman.
"We should take her on for her record in public life and resist the temptation of calling her names and hurling invectives at her just because she is a woman,” she posted on Facebook.
The Ablekuma West MP, however, noted that Prof Opoku Agyeman would struggle to persuade women to support her bid because she signed the 'Montie three' petition.
According to her, it was in bad taste that she was among those who signed the petition for the release of three NDC communicators who had threatened the then Chief Justice, Mrs Georgina Theodora Wood.
"That episode is still fresh on the mind of every woman in this struggle. It was no mean a person than Ghana's first female Chief Justice who had been attacked by the NDC and there was Prof. Jane Naana Opoku Agyeman rising in defence of her party youth who had been convicted for their barbaric actions," Mrs Ekuful stated.
Prof Opoku Agyeman served as Education Minister in 2013, under the Mahama administration.