A method of suppressing ARP packets in a logical network comprising a set of data compute nodes (DCNs). The DCNs are hosted on a set of physical hosts. Each DCN has a protocol address and is connected to a forwarding elements (FE) on the corresponding host. Each FE has a set of flows that specifies a set of conditions to match a set of fields of each received packet and a set of actions to take on a packet that matches the set of conditions. An FE on a physical host receives a packet sent by a first DCN on the physical host and determines that the received packet is an ARP request packet by matching a set of fields in the packet with a set of conditions of a particular flow. The ARP request packet identifies a protocol address of a second DCN on the logical network. The PFE utilizes the actions specified by the particular flow to determine a corresponding hardware address for the target protocol address by searching an address-mapping table that maps the protocol address of each DCN to a corresponding hardware address. The PFE converts the ARP request packet to an ARP reply packet utilizing the set of actions specified by the particular flow, the ARP reply packet comprising the determined target address as a resolution of the ARP request. The PFE sends the ARP reply packet to the first DCN without broadcasting the ARP request to any DCNs on the logical network.