Lebanon, which imports almost all it uses, relies on containerships to bring in everything from refrigerated food to clothing and other consumer goods.
There is no firm date for Beirut port to re-open, and this is a strain on supply chains.
Data from shipping intelligence platform MarineTraffic showed three containerships had arrived in Tripoli in the past 24 hours after being diverted from Beirut, with a further container vessel expected on Thursday and another due on Saturday.
Germany's Hapag Lloyd said it was diverting its services to Tripoli, about 43 miles up the Mediterranean coast from the capital, to discharge cargo bound for Beirut.
'Lebanon is dependent on imports and exports for their needs and we will be diverting services for the moment to Tripoli, which is a smaller port,' a Hapag Lloyd spokesman said.
The spokesman said the company's office in Beirut had been completely destroyed but staff were unharmed.
'Access to the port is not allowed at present so we cannot assess how many of our containers were either damaged or destroyed,' he said.
Beirut's container port has an annual average capacity of just over one million TEU, compared with Tripoli's 400,000 TEU, which could be enlarged to 600,000 TEU and a maximum of 750,000 TEU if more cranes are installed, shipping data shows.
Maersk said it was working with Tripoli port to enable its vessels to call there.
Maersk's Beirut office was damaged and three of its staff slightly hurt. Potential damage to its containers in the port is being assessed.
The Mediterranean Shipping Co (MSC) said it was working on alternative cargo routings, including stops in Turkey and Greece.
The International Transport Workers' Federation said 12 dockers and seven separate seafarers had been killed in the port.