Short answer
No. An open auction, where the item goes to whoever offers the highest price, is allowed, and the Prophet ﷺ himself sold goods by asking who would buy them. What is haram is fake bidding to push the price up (najash), and "penny auctions" where you pay for every bid, which are gambling.
Selling to the highest bidder (bay' man yazid) is permissible. Najash, bidding with no intention to buy in order to raise the price, is haram, whether done by the seller, his friend or his agent. Paying a non-refundable fee for each bid is qimar.
The four schools agree on this.
Explanation
Imam al-Bukhari has a chapter titled "selling by increase" (auction), and under it he narrates that the Prophet ﷺ sold a slave belonging to a man in need by asking, "Who will buy him from me?" The four schools agree that an open auction is a lawful way to sell, whether it is a car auction, a house auction, eBay or a charity auction.
Some people worry about the hadith that forbids selling over the sale of your brother. That applies when a buyer and seller have already settled on a deal and someone steps in to undercut or outbid. In an open auction the seller has not settled with anyone yet; he is still asking for offers, so bidding is allowed.
What makes an auction haram:
- Najash (shill bidding). The Prophet ﷺ forbade it. A seller, his friends or his agent bidding with no intention to buy deceives real buyers. A reserve price stated in advance is fine.
- Penny or bid-fee auctions. Every bid costs money you will not get back, and most bidders lose their fees while one person wins cheaply. That is gambling.
- Haram items, or items the seller does not own.
- Interest, such as buyer finance with interest or interest on late payment.
Bid in good faith: only bid what you mean to pay, and pay on time if you win. For the basic rules of a valid sale, see What are the rules of business in Islam?
The evidence
Quran, Surah An-Nisaa 4:29
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تَأْكُلُوٓا۟ أَمْوَٰلَكُم بَيْنَكُم بِٱلْبَٰطِلِ إِلَّآ أَن تَكُونَ تِجَٰرَةً عَن تَرَاضٍۢ مِّنكُمْ ۚ وَلَا تَقْتُلُوٓا۟ أَنفُسَكُمْ ۚ إِنَّ ٱللَّهَ كَانَ بِكُمْ رَحِيمًۭا ﴿٢٩﴾
O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent. And do not kill yourselves [or one another]. Indeed, Allah is to you ever Merciful.
A sale is lawful when both sides agree freely, as in an honest auction.
Sahih al-Bukhari 2141
Sahih... من يشتريه مني ...
"Who will buy him from me?"
The Prophet ﷺ invited offers, which al-Bukhari places under the chapter on auctions.
Sahih al-Bukhari 2142
Sahih... نهى النبي صلى الله عليه وسلم عن النجش ...
"The Prophet forbade najash (bidding up a price with no intention to buy)."
Fake bidding is forbidden.
Sahih al-Bukhari 2139
Sahih... لا يبيع بعضكم على بيع أخيه ...
"None of you should sell over the sale of his brother."
Applies once a deal is settled, not to open bidding.
Where the ruling is recorded
- al-Hidaya, Kitab al-Buyu', section on disliked sales after the chapter on defective sales. States that there is no harm in selling to whoever bids more, and forbids najash.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Buyu', Bab al-Bay' al-Fasid, section on disliked sales. Same ruling, with the explanation of when outbidding is forbidden.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.